Whereas a first person story is narrated by one of the characters, third person omniscient is narrated by someone outside the story -- specifically someone who knows what everyone is doing or thinking at any given time.
The most obvious benefit of this is tremendous freedom. You can present anything that anyone's thinking in any place. This allows you to tell a tale with fewer words and to reveal information however you see fit. And for some reason, third person feels more immediate, like it's happening right now (yes, even though it's written in the past tense).
But like first person, these advantages are omniscient's disadvantages as well. The freedom to be anywhere, in anyone's head, doesn't mean you should be. You can drain a lot of tension and do a lot of telling (as opposed to showing) if you're not careful.
The other disadvantage is that third person omniscient puts a barrier between the reader and the story: namely, the narrator. In first person, the narrator is part of the story. There's no barrier because the story is being told by it's owner. In third person omniscient, the reader is constantly -- sometimes annoyingly -- aware that they are being told the story by someone who wasn't there.
This can be a good thing. Mark Twain's voice was eminently obvious in his novels, but we liked it (well I did). His commentary on 19th-century southern America could not have been made in first person. With third person omniscient, Twain got to tell us what he thought about (for example) the schoolmaster's pomp and what Tom thought, not to mention what the schoolmaster thought when his "prize student" Tom couldn't recite a single verse.*
So, some tips:
- Find the narrator's voice. This is usually your voice, but not necessarily.
- Don't hide things from the reader just to be tricky. This really goes for any POV, but it's easier to hide information with omniscient so it needs to be said.
- Know why you're using third person omniscient. Again, this goes for any POV, but I think it's easiest to slip into omniscient without realizing it. Use omniscient for its advantages above, not because you don't know what else to do.
* Don't worry if you don't know/remember what I'm talking about. I wouldn't either if I hadn't just gone through Tom Sawyer with my niece.