It's an expensive route, but I swear by
Reason for drums.
Other people swear by other things, but it all comes down to 2 things: the sounds you use, and how you program them.
The sounds:
If you aren't going for electronic noises, you're going to want sounds that are both realistic and dynamic. By dynamic I mean that 5 snare hits in a row should NOT mean the same sample played 5 times. that sounds computery, and people can pick up on it. The are free sample players out there that are capable of loading, say, 5 slightly different snare sounds to be triggered at random on one note.
As for the actual sounds, there are free ones to be found, and I'm sure a lot of people around here (myself included) wouldn't mind sharing the free stuff they've collected, thus saving you the legwork.
The programming:
The best way to go about it, obviously, is to get an
electronic kit and use it to trigger your samples. Not only will this cost you a lot of money, you'll have to learn to play the drums anyway. pff. screw that, sounds like work.
The second best alternative is to
play the drums on a midi keyboard. This will keep the timing and velocity sounding "human" so that all you have left to worry about is the good samples.
If that's too much, then you're stuck sequencing beats with a mouse and a grid in your daw. In this scenario, you're going to have to work on several things to keep it from sounding computery:
1- use an imaginary drummer, and don't make this drummer hit 5 things at once. eg:don't put a hi hat, snare, and tom in the same place, since your drummer can only have 2 arms.
2- look around in your software for a humanizing or "de-quantizing" function, which will take the notes off the perfect grid, and add some randomness to the hits, since real drummers are NEVER perfectly in time (burn!)

This makes a bigger difference than you might think. It's another one of those things that the human ear can detect even if it doesn't know it.
If you don't have this function in your software, no worries- turn "grid snap" off, and enter the notes by hand/mouse, and feel free to be a bit (just a bit) off.
If you have your samples set to sound different with a varying midi velocity, make sure you "humanize" that too.
keep in mind, I aint no drum guru, and feel free to suggest what I may have got wrong or missed.