before actually training, get a lot of stretching in to build up flexibility and prevent any injuries during your training. i always show up to Fairtex early so that i can stretch for a good amount of time before training, and it definitely helps out a lot.
I was never flexible until my dad put me in karate when I was in junior high. Before long, I could put my wrists to the floor when stretching my hams, and I could kick over my head. Doing it will make you more flexible. Just remember to stretch a lot and warm up before class, like the guys already mentioned.
Absolutely, breathing is key. By the time you finish with a deep breath, you can usually go a lot farther during the exhale. Do each stretch about 20-30 seconds at a time, but not longer than 30 seconds. If you're not happy with the first stretch, come back and do it again. You'll get flexible, it really doesn't take that long.