When that base alert reaches to level 3 head back to base immediately. Grab a Machinegun and ammo from supply locker. Run from gate to gate until siege is over. That is how I survive from sieges. If there is a Feral / Juggernaut zombies lure them near gas bottles and shoot the bottle. BOOM! No more of that zombie.

Info: This does not always work. Sometimes those army zombies come and you can't shoot them. You need melee weapons to crack them up.

These missions can be REALLY annoying if you don't know what you do there. My advices: Get at least one squadmate, melee weapon and silencers. Do NOT shoot zombies without silenced weapon. It is like ringing food bell rest to the zombies if you shoot with non-silenced gun. That is about my advices.

Adding to this text: Using silencers is ESSENTIAL for survival. I forgot to put silencer on one mission and bam 20 zombies came.