It kind of bothered me when in career mode, my base was depleted of fuel before realizing how strict the fuel parameters are (and also specifically how almost zero information regarding how to refuel is available. perhaps like 80% of tutorial makers assume this is too rudimentary to warrant a guide, but personally I find the game to be incomplete and very confusing in terms of how to accomplish and do basic tasks). Also, was dissapointed on the lack of guidance in regards to doing repair missions. This guide will cover both. LETS BEGIN BY TEACHING YOU HOW TO REFUEL, then moving on to repairing at the end.

REFUELING (in career)
On your builds, you will have fuel tanks (small, medium, large, or custom) make sure each fuel tank is connected to each other either through piping (T pieces would be ideal) or if the fuel tanks are placed directly adjacent where their circular openings are directly lined up and touching each other. Now, on just one of those fuel tanks, utilize the side that is not hooked up to the other tanks. you will need to place a "HOSE ANCHOR" (found in inventory in build menu) covering that hole. Or, most builds will likely require you to build pipes going out to the side or on top, and then at the end of that refuel "pipe node" so to speak, you will place the HOSE ANCHOR connected to that. YOU ONLY NEED ONE HOSE ANCHOR EVEN IF YOU HAVE MULTIPLE FUEL TANKS. That is true, so long as all your fuel tanks are connected with one main line. If you have some tanks that are not connected, they'd need their own hose anchor.
Still in the build menu, use the select tool (its an arrow on the top of the build menu) and select the fuel tanks by clicking on them. Select which ones you want empty (these will be the ones you refuel, taking home to base a fuel profit) and click and drag the slider to change the fill level. Or, ideally your build should be fuel efficient enough to where you can select all of your main fuel tanks, and simply click and drag the fill levels down to 10% , or 20% or which ever is the lowest amount that you know will be enough to reliably make it to the fuel station without running out of gas mid trip. If it requires 50% or more of your fuel capacity to reach there, you won't be making any fuel profit. Fuel costs between 2-4 dollars per liter. Typically, my runs with my fuel levels typically run me anywhere between 1,000 - 8,000 dollars (expect fuel costs to eat into your mission profits to an extent).
Now for the difficult part. Adventuring out to the miniscule amount of pump stations, which are spread far and wide. On the map, look for a gas pump icon that is black (green ones repressent stations where you sell liquids/ stuff. Black repressents purchasing for yourself). Check to make sure it is either diesel or jet fuel (jet fuel stations are rarer, and typically further to reach depending on seed).
Now, if all is said and done, and you complete the quest of just arriving directly at the foot of one of those fuel purchase stations, its time to consume. Grab a red "hose", which can be found on the pump stations themselves, or you can place one in your build. Immediatly you will notice that you can hit "r" to toggle open/ close the hose itself. Practice messing around in both modes to learn what it's like and what it does. You can still purchase fuel and refuel even when the hose is technically "closed" for the pump stations force kinda just makes it work regardless. Take the hose, and look at the fuel station's winch/ nozzle area and click. You should see the hose now connected to the purchase station. Now walk to the "hose anchor" on your build and click. You should now have a hose connection between pump station and the vehicle. Walk to the pump station, and there are toggle buttons built into it. Select "pump out" or "pump" or "on" or something of that nature. The refuel process should be active. You can hit the map button and view your total money dropping down which repressents the fuel cost. You can also go to any dials on your build that monitor the fuel content level . When finished fueling, hit the same pump button you hit earlier. Now disconnect the hose. If you used the one from the pump station, I suggest putting it right back where you grabbed it. To my knowledge, pump hose slots will not automaticlly replenish. So don't be messy and leave stuff lying around.
You have collected the good stuff now. Begin your trip back to the base in which you want the excess fuel to be stored. WHEN YOU ARRIVE AT BASE, you do not need to fiddle around with the hose or the pump. Simply park the vehicle in the build zone tied to that base, and run to the workbench and despawn the vehicle. ALL FUEL IN VEHICLES WILL AUTOMATICALLY OCCUPY THE BASE FUEL PUMP AFTER DESPAWNING. On the same note, if your base fuel station is down to say, only 1,000 fuel, and your max fuel level on your vehichle should be 2,000 fuel, well, spawning that vehicle in you will see that it only has 1,000 fuel. That is because your base does not have the amount of fuel necessary. That is normal. If this is complicated or confusing I'm just really sorry the game does such a piss poor job of explaining critical, fundemental, or crucial aspects.

Now, if I had to guess, if you are reading this guide you are likely at the coastgaurd beginner outpost, the first one most players would start at / do start at. I have some bad news... refueling from here with your vehicles is not ideal, given it's a micro build zone and an island. You have 2 ish options...
1, amphibious craft. Since the majority of the games fuel purchase stations are on ground and only accessible by being on ground (absolute horrible game play design by the way) you will need your refuel boat to be capable of driving up on land in order to reach the fuel pump and then making the return trip. The problem is... the fuel station near "Holt" town, which could likely be the closest one to you, the river and majority of the coast line is MILES of this god awful, steep, grey like mini rock cliff. In terms of gameplay design, this infuriates me because the transition from water to land is 90% of the time way to steep to get any sort of ground/ water craft up and over this ledge (without flipping and toppling over into the water). (Again, awful and frustrating map design that is detrimental to simple refuel operations and people who like amphibious craft)
Option 2, utilize a micro small helicopter with landing floats at the bottom, one that fits within the build zone of coast gaurd beginner outpost. Spawn this in, and instead of starting the engine immediatly and dinging up the rotors, just swim at it in the water and push it out of the tiny water garage until its cleared. Or , hook it up with a rope and swim it out that way. Once in the open water area, hop in, fire it up, and fly to the fuel pump station. land as safely as you can and as close to the station as possible, fill up, then fly back.
When returning, you can do the safe procedure i mentioned earlier, or you can crash land into the water garage area if you want, it won't matter if you ding up the rotors and destroy it. As long as the bird remains within the build zone limits, all you have to do is despawn it from the workbench and all fuel that was in it will automatically go to base fuel. You are not charged for vehicle damage. (General note: despawning any vehicle from the workbench refunds the entire price of that vehicle. Have a 5,000 dollar boat? spawning it costs 5 grand. Finished with it and have returned? despawning gives back 5,000 dollars. That one burnt up boat you have flipped about 100 yards away from goofing around? yeah, so long as that boat carcass is not back and despawned , you have money wasted).
Here is a link to a perfect chopper I have built that you can spawn within the coastgaurd beginner outpost build zone, and is configured with ready, waiting, and empty fuel tanks. Chopper costs 9,200 dollars to spawn tho, so be aweare of that (if you are down to 10,000 dollars total in game, you'd only be able to buy 800 dollars worth of fuel and so on). https://steamproxy.com/sharedfiles/filedetails/?id=3299458327
I suppose the third option as well is to just have a base that is on the main land or where buying fuel can be entirely done through ground transport, and not water. With proper base locations you should be doing most of your refuel runs with planes or helicopters specifically. My only comment after saying this, is just sorry. I'm sorry that these are your ♥♥♥♥ options. Ideally all fuel locations situation on ground should have a secondary water access pump station in the same town or area, where the pump stations can reach regular boats. But nope. I didn't design the game.
A general refuel note, you'll probably notice that the hose provided in game, when connected to stuff it has a patheticly short length and will rubber band inwards like its shrinking. If it was a good game, it would just be a hose that has the lenght of about 40 feet (which would prevent many un-deserved and uncalled for flip overs) but anyways, to mitigate this or solve this, start attaching hose anchors to the end of winches. and use the winch to extend or retract the hose lenght to be more functional. (the winch process specifically building it yourself for your own build is complicated and requires its own guide).

last thing ill say about refueling, for early game / while you are battling fuel scarcity, i highly reccomend using builds that utilize either a single small diesel engine, or two small diesel engines. the small diesel engines run way more efficiently in terms of fuel consumption. also jet fuel is like double the cost. so yeah. Small diesel engines are the way to go. bigger engines and jets are more suitable late game after you have aquired and established a good foothold in terms of finance and base(s) ownership.

Thankfully if you are looking to complete the repair missions, this is much simpler and will not take up a lot of time reading at all.
In your build menu, go to inventory. Search "welding"
You will select the "welding torch" and I also reccomend placing down a second one, called the "under water welding torch". the under water one allows you to repair while currently in water. The other welding torch does not let you use it if your character is in water.
Now that your build has the welding torches, drive to the mission repair objective. When you arrive, there should be some notification whether on screen or hovering over it on the map, as to what specifically needs to be repaired (if its a radio , thats usually on top) you might need to repair things like a rain sensor, or the dashboard, so be it.
To repair it, simply hold the welding torch and visually scan the service vehicle for signs of damage / scrapes. Now, left click whilst looking at the damaged area and holding the welding torch. By defualt, the torch emits a constant whine noise. But, if something is being repaired you will hear a clickity clackity noise. Keep holding left click until all clickety clack noise goes away. there may be multiple areas that need to be repaired before the objective is registered as comlete, and when it is comlete, you will see money being rewarded.

This may sound painfully obvious, but again the game only holds your hand and guides you for the initial rescue mission. It says nothing in regards to other mission lay outs and it is basically what I would consider an incomplete tutorial. Repair objectives are nice because they are so fast and easy to complete, but be advised the pay out is not that great, so make sure you only go to ones that are somewhat close by, as fuel costs can and will eat into profits. It might be possible to get a repair mission so far away, that if you actually did it, and depending on the fuel economy of the build, you end up losing money on fuel costs.
Here is a link to a nice and simple boat i've made that has repair tools on board behind the captain chair
https://steamproxy.com/sharedfiles/filedetails/?id=3280793295