Varys is the spymaster (coolest title ever) for King Robert, so he gets reports from all over the world. Varys has no family that we know of (usually the family tree of a eunuch is pretty easy to draw) and no real friends, it seems.
Here's the difference between Littlefinger and Varys (at least, according to Varys): they may both be scheming little manipulators, but Littlefinger serves only himself, whereas Varys serves the realm (59 Eddard 15.67). Unfortunately, Varys doesn't give us a lot of proof of that. For instance, he tells Eddard about an assassination plot against King Robert, but only after the plot has already been avoided thanks to Eddard himself (31 Eddard 7.130).
And we might want to ask what Varys means by "the realm" anyway, since Varys has served one Targaryen king and now one Baratheon king. Is he claiming to be neutral? Hmm, we're not sure we buy it. In fact, when Arya overhears two men plotting underneath the castle, one of them reminds us of Varys: he's "oddly familiar" to Arya (33 Arya 3.39) and wearing something similar to his disguise when he visits Eddard in the dungeon (59 Eddard 15). And what Arya overhears sounds like a plan to bring the Targaryens back to the throne. So is Varys a Targaryen loyal? Or, oh no, is he double-crossing the Targaryens? Oh boy.
Now, Varys has his reasons for acting the way he does: he has a role to play (see "Society and Class" for more on that) and he only has his limited power. As he notes, he doesn't command any warriors, only whisperers. That seems like a pretty good argument to us and yet we can't quite trust him. Do you?
Petyr may be a liar and a betrayer, but Varys has seemingly supernatural spying abilities. He is a master of disguise: when he sneaks into Eddard's cell dressed like a jailer (excuse us, we mean "gaoler"), Eddard asks him, "what sort of magician are you?" because his disguise is so good that it seems like magic (59 Eddard 15.26). Varys gives a clue about this ability with disguises when he mentions that he used to work for a group of actors (excuse us again, "mummers") (59 Eddard 15.39). (Yay for old-timey vocabulary.)
Varys definitely has more than just a make-up kit. As Catelyn notes, "Varys has ways of learning things that no man could know. He has some dark art, Ned, I swear it" (21 Eddard 4.98). Now, if this were a historical novel we'd just say, "secret passages, network of spies, yadda yadda." But since this is fantasy, we might wonder: does Varys really have some supernatural powers?