"Please drink water."
You should do a little research on て-form, either in Tae Kim's or even on youtube. It will help you loads and make japanese a lot easier when you get it because you use it to a loooot of stuff. Here, to make a polite request that you drink the water.
So yeah, のんで is the て-form of のむ. Verbs ending in -む change to -んで.