Everyone wants to be Gene Krupa or Neil Peart on the first day, but it just isn't going to happen. Learning to drum is a process, and not usually a fast one. The key, along with proper lessons, is patience and trying to emulate what you hear your favorite drummers playing. Then listen to yourself and be critical; be overjoyed when you improve, but also be a tad hard on yourself when you don't. Trust me, if you stick with it, one day it all just clicks and you tell yourself, "Hey, I'm not half bad!" Until that day comes, though, please take your time and don't rush your drumming - you'll pick up bad habits that are very hard to change later.
Get a good teacher.
A music teacher is easy to find, however, to get an efficient one, you need to check certain things. Before you hire a drum teacher for lessons ask him about his previous experience. A person with good experience in both teaching and performing music at events is ideally the best teacher to hire. This will give you a good platform to learn the instrument and your teacher’s experience will help you become a good performer. Be aware, a good drummer may not be a good tutor. So it is essential that the tutor you hire have a good experience of both giving lessons and playing the drums. Many musicians still take lessons and keep improving and inventing music. An active tutor will always be more beneficial than a tutor who has given up playing.
Go slow.
The speed will come, for sure, but making yourself drum as fast as you can every single time you practice will hurt your play in horrible ways. Take your time, making sure you have great control before you attempt to speed up, your future band will THANK you for it.
Work on your meter.
Everyone loves a drummer who can do insane rolls and double bass beats, but unless you can actually play in time, all the fancy drum stuff in the world doesn't mean much. Almost every band I've encountered would rather have a simple drummer who keeps great time than a monster who can do 47 different kinds of amazing rolls and solos but can't find the beat to save his life.
Get a video or two.
Videos can give lessons on hand / stick technique, foot positioning, snare work and actual beats are all great to watch if you are just starting. To be honest, I know a few veteran drummers who could use some video lessons to brush up on their chops. Spending a few dollars NOW on a DVD can prevent you from trying to change a bad habit years from now, when it will be much harder to accomplish.
Play to the radio.
Slap some headphones on and put the dial on your favorite station or play a CD. Playing with recordings is a great way to learn because the tempo stays steady no matter what. You'll know real quick what you need to work on when you find yourself drumming way ahead of the beat in an already fast song. Try different stations and styles of music as well, don't just drum what you want to play. In one hour of drumming you could play some oldies, some funk, some punk, some country and some alternative. Heck, when I was learning I'd even play to the Spanish stations because I couldn't understand what they were saying so there were zero cues for when stuff was coming up in the song other than the music itself.
Get a practice pad.
These little gems are very inexpensive at around twenty dollars and will allow you to practice drumming at night when mom wants a quiet house, when traveling, while watching TV or really anywhere you have a little stick room. They usually consist of a wooden base with a rubber top of varying density and are about the size of a snare drum head. You can set the drum pad on your lap, a table, a chair, a bed or anywhere else that is comfortable and you won't bump into things. I personally find these are especially effective with headphones or while listening to the stereo.
Get the basics down first (know your rudiments).
A drum rudiment is basically a sticking pattern. Every sticking pattern you play on the drum set is derived from different drum rudiments. Most are very common patterns that you are well aware of like the single stroke roll, double stroke roll, paradiddles, and flam strokes. Some are more complex and difficult to play. The next time you play the drums, you should look and see what rudiments or sticking pattern you are actually playing. Drum rudiments are the essentials of drumming; they should be practiced by drummers to increase their stick control, speed and independence.
Learn how to tune your drums.
A well tuned drum sounds exponentially better than just slapping a head on and going. In fact, it greatly increases the life of the drum head if you have it installed the way it should be. There are videos all over which can teach you the proper methods, or you can talk to an experienced local drummer.
Try playing soft once in awhile.
Yea, I know it's fun to bash the things, and you think it looks cool when drummers break sticks on stage left and right, but it isn't good technique and it can be harmful to the equipment. Play around with this a bit, try really smacking your snare good and hard, then medium, then rather soft. I think you'll find that the difference isn't all that great, and if you try playing softer you'll see improvements in speed and endurance almost immediately. Besides, sticks and heads are expensive, why not keep them as long as you can?
Don't forget about the internet!!
The internet nowadays is an invaluable sourse of information regarding drum lessons. Check out sites like YouTube, vater.com, evansdrumheads.com, etc. for information on sticks, drums, drumheads, hardware, lessons...you name it. Simply running a search on Google for "drum solo" or "drum lessons" will bring up a million websites for you to enjoy!
Above all else, remember this: "If you're not having FUN, you are doing it wrong!"