Sticking is simply the combination of hand swings that you use to play a pattern. For example, when you play a simple eight note roll on the red pad or two notes across all four pads, you would usually use the sticking RLRLRLRL, where R indicates using your right hand and L indicates using your left hand. On a more complicated roll, where there are triplets thrown in, it's often easier to use your left hand twice to hit the latter two notes of the triplets. For example, on a stream of triplets, the sticking becomes RLLRLLRLLRLL. As Chad Birch notes, it's a technique that is more developed naturally rather than something that is taught.
However, learning proper sticking is primarily important when you want to start aiming for high scores, as odd stickings mainly show up in drum fills. If simply passing songs is your main focus, the main thing to do is practice. High tier songs like Bodhisattva and Painkiller are absolutely killer on your arms and legs until playing on the RB kit becomes more natural for your body. Make sure that you keep a light grip on the sticks(although not too light; dropping your sticks is the worst) and routinely practice swinging your wrist gently to get that natural stick movement you'll need to play faster beats. It's also important to keep the bass pedal pressed in-between stretches of bass notes, as opposed to released, so your foot can rest and you don't have to put so much energy into hitting each bass note. Welcome To The Neighborhood is a good song for developing endurance.
Other high tier songs such as Panic Attack and Shoulder To The Plow feature lots of interesting patterns that are difficult to decipher for an unadjusted eye. There are two things you can do that I can think of to drastically improve your performance on these songs.
1. Practice Mode
If you simply don't understand what's happening in a pattern at all, taking the song into Practice Mode and playing it at half-speed can give you an initial impression of the beat and the spacing of each note. Use the initial half-speed plays to figure out what sort of sticking you should use. If your sticking feels even slightly unnatural at half speed, it's not going to work at full speed.
2. Watch A Video
Many people have uploaded FC videos to YouTube that show a split-screen view between the RB kit and the drummer. This can give you an impression of how the beat or fill should sound at full speed. Try to commit that sound to memory and try to replicate it. Smooth out your replication, note their sticking and you've got it.
In the end, though, none of this is really vital; keep playing songs and smoothing out the sections where you lose the most points, and you'll definitely see your stars increase at a rocket pace.