うまい umai is a multi-meaning word, which generally means 'good'.
For instance, it can be used to say someone is good at doing something.
洋子はピアノがうまい ようこはピアノがうまい yoko wa piano ga umai - Yoko is good at (playing) the piano
It can also mean something tastes good or is delicious.
このラーメン、うまい！ kono ramen, umai! - This ramen is delicous!
A third usage is to say a procedure is (or should) go well.
ビルは今日真由美と初デートだ。うまくいくといいな。 ビルはきょうまゆみとはつデートだ。うまくいくといいな。 - Today, Bill has a first date with Mayumi. (I) hope it goes well.
However, there is one caveat for using umai. Except for the third usage, umai is considered to be a very informal and not-too-polite word. It should only be used by males in informal situations. If females use it, they are considered to be a bit rude or mannish. So, if you want to stay polite, you have to use different words:
For the first usage, 'is good at something', use 上手 じょうず jouzu
Example: 洋子はピアノが上手 yoko wa piano ga jouzu
For the 'tastes good, delicious' usage, use 美味しい おいしい oishii
Example: このラーメン、美味しい！ kono ramen, oishii!
(An even more informal way to say うまい is うめえ umeh. I had fun for a few years telling The (Swiss) Guy that the word for delcious was うめえ, and watching my Japanese relatives doing a small double-take when he said it. I did get found out eventually...)
Opposite meaning words
The opposite meaning word for うまい differs by the meaning.
うまい (as in good at something) -- 下手 へた heta
うまい (as in delicious) -- まずい mazui
As for the third meaning, while まずくいく is not used as a phrase meaning 'go bad', まずい is used to mean 'a bad situation', or simply 'uh oh' or 'oh no'.
Example: まずい、財布を忘れてしまった。 まずい、さいふをわすれてしまった。mazui, saifu o wasurete shimatta. - Uh oh, I forgot my purse.