I won't actually have the set 41 f2l cases and algs here because I don't use them.  I highly reccommend learning F2L intuitively. The basic premise is you use 3 moves to create a pair and then 3 more to insert with U adjustments thrown in to get 8 moves max for a pair. Any case that involves more than doing just that then you can learn an alg for it.
In OH my F2L can be around 10 seconds so it is not too much slower than with both hands but it still gives you more time to think and plan the moves out more. With that it provides oppurtunity to do more effecient things such as planning an x-cross, multislotting and non-matching pairs.  Maybe it is just because I don't practice with both hands but with 2 hands I do not think of these things but with OH I employ all of these.
The things listed above are pretty advanced and I don't use them too often but what is most important and can help out in every solve is learning to create pairs from many different angles and in different ways.  I highly reccomend taking time and going slow thinking through your F2L, not for speed, to look for different ways to pair up you may not catch at full speed.  
Another useful thing is cross on the left. Instead or doing a (u) rotation to move the empty slot to the right side a (f) rotation can be used to switch to cross on the left making putting pairs in on the left easy.  An (f) turn takes less of a regrip to do since you don't have to move your thumb and other cube holding fingers to new faces as you do with a (u) rotation.
If I ever get good with using images and such on this site I will add a table with a few tips for strange cases and pairing in different ways.
 

Like many people I was only told of the Fridrich method so that is the method that I use and the advice here mainly applies to that method. However I would certainly recommend checking out other methods to solve the F2L! The main methods to do this are Roux, Petrus and Heise. Unfortunately for Roux I have to cross it off the list but simply because this is a OH site. It has a but to many M turns to be a good OH method in my opinion. You are left with Petrus and Heise. Both are brillant blockbuilding methods. The main reason people count out these methods are that "they require too much thinking". This is not neccesarily true people are just not used to thinking in this way since Fridrich is all they know. I say its not neccesarily true but you do have to think a lot to solve this part optimally. Luckily for us we are solving OH so have that extra time! Blockbuilding can be challenging especially since you do not have countless guides and tutorials to help you but search around and you can find all the help you need.