Going into the studio for the first time is an awesome experience, so congrats on having that opportunity. Here's a couple tips that should get help you on the right path:
Practice-Playing-Stuffs:
1) Hone-in on your playing BEFORE you get in the studio. Now is not the time to get fancy and creative. You should be rock solid once you step behind the kit. If you've got parts that are too difficult, or parts that are just sloppy, either get them locked down now, or simplify them. Make sure everything you play is clear, clean, and sharp. Don't make the engineer waste tons of time trying to cut and paste your parts together because you couldn't play them correctly or in-time.
2) Click tracks - I absolutely loathe playing to clicks, but it's a necessary evil. But here's one method you can use that takes some of the robotic feel out before you get in the studio:
Let's say you're playing a rock tune with a tempo at 160:
a) Start by playing your song through with the metronome set for quarter note clicks at 160. Analyze your playing, and keep at it until you're in lock-step with the metronome.
b) Now, cut the clicks in half. If you've got a metronome that lets you set a different subdivision, set it for half notes at 160. If you've got an old clickly one-setting-fits-all metronome (like I do), just cut the time in half to 80. Now play your song through, again analyzing your playing until you are in lock-step with the metronome.
c) Now, cut the clicks in half again (whole notes, or time set to 40). Play through and analyze again, until you're in lock-step.
If you can do this with every song, hearing only the whole note clicks, you'll be good to go. Just ask the engineer to set the click to whole notes, and rock it out.
Before you go into the Studio-Stuffs:
1) If you can, have someone give the engineer a clean copy of your music up front. This is especially helpful if the engineer is unfamiliar with your material. Obviously, it's not going to be "studio quality", but if you can get your bandmates together to record a decent live demo of your stuff, it'll be a great help.
2) Tune up your drums, and clean up the sound, wipe down your gear! Make sure you've got decent heads, no rattles in the hardware, no squeaks in the pedals. Leave the broken cymbals and dead drums at home. Pay someone to fix stuff if you have to. Going into the studio with broken gear is like entering a race with a broken down car. Don't do it!
Also, don't piss the engineer off by getting his clothes filthy while he's trying to place mic's because you didn't wipe the 9-month-old buildup of dirt and grime off of your bass drum.
3) Lay out a plan of the order you want to record your songs. Here's an example:
a) Start with the song you are most confident playing. Something that's strong, pronounced, medium tempo, with a big, bold sound. This is going to help you get in the groove, and help the engineer lock into the recording. Also, this is the time when you may have to stop a few times for mic adjustments, so you want something you're comfortable with playing a couple times.
b) Move to more articulate and dynamic songs next. If you've got slower or more mellow songs in your list, put them here.
c) Finally, end with your up-tempo stuff. It may seem a little counter-productive, but you want to be recording this after you're warmed up and locked in. Plus, putting these last will keep you from getting all jacked up or tired out early on.
4) Get a decent night's sleep, and don't get too crazy with the extra-curriculars the night before. You don't want to be hung over. And stay away from spicy food. Unpleasant aeromatics aside, you don't want stomach and ass-cramps the next day.
Studio day-Stuffs
1) Show up when they tell you to show up - 5 minutes early is okay, but 5 minutes late isn't. And don't be the dude that shows up two hours early, roaming around in the parking lot.
2) Make sure you have spare sticks, maybe a spare kick-drum mallet and beater head for your snare, a drum key, something to drink (water or gatorade or something that'll keep you hydrated), maybe a couple granola bars to snack on. No booze - save that for later.
BONUS - Shower beforehand, wear clean, comfortable clothes, and bring a clean towel, an extra t-shirt, and an extra pair of socks. You're probably going to be a sweaty mess before it's all said and done, so there's no reason to start that way.
3) Take your practice pad, and warm up before you sit behind the kit. Time is money, don't waste $50 getting ready because the clock started running and you were still cold.
4) Listen to the engineer's instructions, work with them, and be open to their recommendations. I've seen a lot of drummers get all snippy because the engineer didn't like their snare sound, only to realize later on that the old beaten up studio snare ended up sounding like a million bucks on the recording. Don't think about something being right or wrong before you try it - give it a shot, listen to the result, and then make the decision.
5) When you finally get set up, locked in, and ready to play, take a minute to relax and regroup, get everyone else out of the room, and let 'er rip!
Good luck!