Just as a further explanation, there are 2 "prayers" in islam.
One is salat, which is more akin to a mini mass, liturgy, service, etc. This is the one most people immediately associate wtih islam - the bowing and the prostration. The Prophet (saws) told us to "pray as you have seen me pray." There is a set script for this prayer, supplications in arabic and chapters recited from the Qur'an.
The second prayer is dua, which is what is most analygous to the english word prayer. It's a supplication, praising God, thanking Him, asking Him, etc.
Salat should be prayed in arabic. As previous posters wrote, you could pray it in english if you're absolutely unable to do the arabic, but the end goal should be to learn arabic. When I was learning salat, I had a set of index cards. On it, I had one line written in arabic, and another in english. I would stand for my prayer, holding the cards in my hands, and then I would read the line of arabic aloud, and then read the english meaning to myself. After some time of this, not only did I have the arabic memorized, but I knew what I was saying too :coolious:
Dua can be in your native language and/or arabic. There are duas that the Prophet (saws) made that we are encouraged to learn, but nothing is stopping us from us pouring our hearts out to Allah (swt) in the language we're most comfortable in.