FM stands for fewest moves, and OH stands for one handed. These are 2 ways to solve a 3 by 3 that are in the WCA. The current record for 3 by 3 OH is 6.82 seconds by Max Park. The current record in the WCA for 3 by 3 FM is 16 moves by Sebastiano Tronto.
When you are trying to solve a cube using the fewest moves possible, you should try to use the Roux method (roux is pronounced "roo"). Just like CFOP, there is advanced Roux and beginner Roux. If you want to learn the roux method, go HERE. If you want to learn some tips on how to get faster and advanced roux, go HERE. If you want a good roux method website, go HERE.
Fewest moves has a different amount of moves in a scramble. If you go to cs timer, (see on timing yourself page of this website) you can change your solve into 3 by 3 fm. The scramble is a couple moves longer.
Usually, when solving a cube one handed, you use the opposite hand that you write with. (if you write with your right hand, use your left hand.) Also, you want to make sure your cube is smooth. If your cube isn't good, it could be harder for your hand.
For OH solving, you still use the same method you use for 3 by 3. If you use CFOP, there are alternative algorithms that make one handed solving easier and faster. If you want a link to One handed OLL algorithms, go HERE. If you want a link to one handed PLL algorithms go HERE. If you use the Roux method as your main method, go HERE.
You can use a flat surface in front of you to help you with your turning. This could be a lot easier.