Firstly the keys F2, F3. F4 will all get rid of certain aspects of your HUD. Including the rider's attributes etc. The button that gets rid of the white circle underneath your rider (and name above him) is # or ~. You will now have a screen with just the riders!
EDIT: Eyoflur has very helpfully told me that you can also press CTRL - U to fully disable the hud instead of pressing all the F keys!

There are also many ways to change the camera angle. Pressing F5 gives you the default view yet the other F keys will give you other views. Some include helicopter views, finish line views or views up alongside the rider. If you hold the middle mouse button on your mouse and move your mouse at the same time you can control the camera giving you complete control of your screen!

And that's that! Pretty simple and you should have pretty snazzy looking screenshots now!!

EDIT: To take screenshots in game, simply press F12