If you have only been at that school a semester, it might be difficult to get a good letter from anyone. Regardless, here is what I suggest:
If you want to ask your professors at your school for letters, just e-mail or ask in person, the (two?) that you know most. Its best that you select the ones that know you can say more than "He/She was good in my class..." When you do, explain your situation, your interests in REUs, etc to them...
This may not sound like advice, but honestly, its the best I can think of...just ask! The sooner you ask, and the more apparent you make your situation, the better.
Also when you ask, tell them roughly when the dates are, and ask if they think they could write them by then. I suggest doing this because if they hesitate (using the timeline as an excuse), they probably don't want to write one - a sign of a bad letter. Plus, its just the nice thing to do.