I have recessed lights that are controlled by two switches. They used a black, red and white wire for each switch to a junction box then used a 14-2 wire to the recessed lights. My question is how do I add another recessed light to it and can I use a 12-2 wire or do I have to use 14-2.
You can hook another recessed light in parallel with the first light. You can either run another cable from the junction box to the new light, or from the first light to the new light.
There shouldn't be a problem using 12/2 if that's what you have on hand, but 14/2 is typically used and is cheaper.
Remember to turn the power off, and verify that it is indeed off before beginning work. And as always, if you don't feel comfortable doing the work, don't have the proper tools, or are just unsure of what you're doing. Call an electrician.
Yes you can add your new line from there (if there is room in the junction box) to feed the new light. Alternatively you can run you new line from one of the fixtures.
You are allowed to use thicker wire. 12 gauge is rated for 20 amp circuits but it is OK to use it on a 15 amp circuit (I assume that is what these lights are on because the existing wire is 14 gauge).