How do you put in an L shaped nose ring?
Also to know is, do L shaped nose rings fall out?
The main disadvantage of L-shaped rings is that they often fall out easily. Their level of security cannot be guaranteed like the other types of nose rings. Again, if you don't want a nose ring that would be too visible, you should consider other types other than the L-shaped types. L-shaped rings are very conspicuous.
Keeping this in view, what type of nose ring stays in the best?
A nostril screw is the way to go. Flatback labrets can be good, but most nostril piercings are small gauge (20g - 18g) and it's hard to find that style in such a small size. A nostril screw has no threading to come undone, and, in my experience, is very comfortable to wear in your nose.
L-bends will fall out pretty easily (but you can make them more secure by wearing an o-ring on the back), screws stay in better, and labret studs make the most secure nose jewelry - but you may need help installing them since the jewelry is inserted from the backside of the piercing (inside the nose).