First things first, learn how to properly spell restaurant. R-E-S-T-A-U-R-A-N-T. Inexcusable, IMO.
Some things Steven said were right, others were a bit off base from my experience.
1. What kind of restaurant?
Let's face it, your chances of walking into a 4 star restaurant with zero experience/references and landing a gig are slim to none. The worst thing you can do is have an unrealistic outlook and set yourself up for failure. Look for the mom and pop restaurants that are locally owned and try and stay away from chain restaurants. It can be done (my first restaurant was a corporate owned Red Robin), but not as easy due to all the red tape one must cut away first.
So, locally owned family restaurants are your best bet right now. Maybe look for places that have a kids night or something where you might be able to sell yourself as a nice addition to that.
2. Dress and hygiene. This shouldn't have to be mentioned, but sadly you'd be surprised that this isn't common knowledge. Go in there well groomed, nicely dressed, smell good, good breathe, hands clean (no nail biting!), clothes ironed and not wrinkly, etc. First impressions are EXTREMELY IMPORTANT HERE, and can make or break EVERYTHING!
The main part of Steven's post, I feel I have to address this specifically as I feel it is way off base and inevitably going to come back and bite you in the ass.
You need to approach them in a professional manner, dress smart and ask them politely that you would like to speak to the manager. Introduce yourself, and show him some magic, explain how experienced you are and let him know how you will be suitable and great for his business. Leave him with your business card, and let him know you will perform on a trail basis for free to see what he thinks.
First things first, whether you choose to use the 'cold calling' approach or not, that's up to you. I've never done that and I'll explain why. I am not selling magic tricks when I approach a restaurant, I'm selling a service to help benefit them. I run a business and must treat it as such. In the business world, meetings are set up. I've always called the OWNER or GENERAL MANAGER to set up a meeting. I feel that by walking right in there, you're already at a disadvantage as they may be busy, irritated, in a bad mood, and they're DEFINITELY NOT EXPECTING A MAGICIAN! To show up unexpected and so sudden already puts up at a disadvantage that can be easily overcome by just calling to set up a BRIEF 5 minute interview during a slow part of the day, morning, whatever.
Secondly, when you call, don't ask to speak to the manager. Your first call should be to find out who the GM/Owner is and when they'll be in, and then hang up and wait a few days. The next call is to set up the meeting. Call, ask to speak to so-and-so, tell him who you are and what it's regarding (performing in his restaurant!) ask if you can take 5 minutes of his time to come in and show him the many benefits of having live entertainment such as a magician.
On that note, Steven said: "explain how experienced you are and let him know you will be suitable and great for his business."
Let's be honest...you have no experience. If you did, you wouldn't be asking these questions. To try and convince someone that knows the business inside and out that you're experienced in restaurant magic, when you've never performed in a restaurant EVER, is just a very bad thing to do.
Also, DO NOT OFFER TO DO ANY MAGIC! Yes, that's right. If he asks, tell him that you'd rather come in on a night he will be there so that he can see first hand how the guests react to the entertainment. If he still insists, show him 1 (ONE!) trick that is short and strong and practically fail proof. But still, insist on the trial night, and make it a night HE WILL BE THERE! He's the one in the position to hire you, so make sure he sees benefits of having a restaurant magician first hand.
IMO, the main mistake most younger performers make when trying to get a restaurant gig is they focus entirely way too much on the magic aspect, and not enough on the business aspect. I run a business and treat it as such. I offer a service to my clients that they need. Don't build yourself up as this super magician, but inform him of the many $$$benefits$$$ to having you perform in his restaurant.
Take it or leave it, but that's my $0.02 based on my experience. Some resources I recommend you invest in...
Jay Sankey's dvd, THE REAL WORK ON RESTAURANTS AND BARS.
Kozmo's dvd, LIVE AT THE JAIL HOUSE.
THE MAGIC MENU! (any issues you can get)
Anything by Paul Green, Kirk Charles, Jim Pace, Eric Henning (If you're serious about this, check out TIPS by Eric Henning...a great book that will save you a lot of headache in the long run!), and many others that I know I'm forgetting right now. Just got home from my rest. gig and am beat....
But seriously man, best of luck to you.

Steve