You need a road bike with "road" dropouts. Remove the chain and the rear derailleur. Take the outer chain ring off and replace the chain ring bolts with track chain ring bolts. I use a 42 tooth front chain ring on my fixed gear bike. Notice that this means leaving the front derailleur on. This helps to keep the chain from jumping off.
You now need to make or buy a road rear wheel that has been converted to use a track cog. Because you cannot easily float over bumps, the rear wheel is going to take a beating. I use a heavier than normal clincher in the rear ( and of course a clincher in the front ). To make one, you need a rear wheel that uses a screw on freewheel ( i.e. does not use a cassette ). Remove the freewheel and screw on a cog. Here is the part that takes some time: you need to change the spacers in the axle, moving the hub to the bike's right, so that the cog is directly in line with the inside front chain ring ( though "pretty" close is usually good enough ). There is a magical sure fire way to do this: F**k with the position of the washers until the cog and inside front chainring line up properly. Obviously, as you move the hub to the right, you also need to be changing the wheel's dish to the left.
When you have finished making the wheel, put the wheel in the rear dropouts and put the chain on so that the wheel is in about the middle of the dropouts. The chain tension should be not firmly tight, but not loose enough that the chain can flop around and jump off. If the chain is too tight, you will hear a grinding noise. Proper chain tension is just "below" the point where you start hearing a grinding noise. Or put another way, when chain will not feel like it is "binding".
Did I tell you enough times: "You cannot coast"? I guarantee that you will forget I told you: "You cannot coast", and then you will coast once or twice and then you will learn this lesson. When you coast, the rear wheel will jerk up off the ground and it will scare you. The way to prevent going over the bars and crashing is to: (1) relax your legs, (2) pull on the handlebars like you would do arm curls in the weight room, and (3) resume pedaling when the rear wheel contacts the ground.
Track bikes use a lock ring to secure the cog to the hub. Using a road hub and cog means it is impossible to use a lock ring because there are no counter rotating threads on a road hub. The solution to securing the cog to the hub is (1) use almost no grease on the cog or hub, and (2) after putting the cog on the hub and properly mounting the rear wheel on the bike, STOMP on one of the pedals several times in a forward pedaling motion. This and just riding the bike will ( almost ) lock the cog to the hub. I say almost because since there is no lock ring, it is possible, but very improbable, that the cog could unscrew. If the cog does unscrew, it will just spin harmlessly on the axle. Use your two hand brakes on the bike and stop. Then put the cog back on the hub's threads and lock the cog to the hub as described earlier.
Gearing depends on terrain and the wind. I used to live about 20 miles north of Chicago in Highland Park, Illinois. The roads are small rolling hills that are lined with trees. The small rolling hills are absolutely perfect for riding fixed gear on the road. You have to focus on pedaling all the way around the circle going uphill and you get to really spin on the down hill, without getting out of control. The trees usually prevented the wind from being too much of a headwind or tailwind. When it was windy, I would bring another cog in a plastic baggie and change cogs when the wind changed. Now I live in Aurora, Colorado. The hills are alittle bigger, but there are no trees and there is a lot more wind. So I just freewheel during the windy time of the year: April, May and June.
Remember "You cannot coast"? It means some things regarding the driveability of the bike: (1) because you have to pedal through turns, you can't put the inside foot up and coast through the turn. This means you must learn exactly at what angle of lean, will the inside pedal nick the ground. When the pedal nicks the ground, the back wheel will lose some to all of it's cohesion with the pavement, possibly causing the back wheel to slide out alittle. (2) the bike will in general, drive a bit sluggishly meaning it will be more difficult to turn (3) when you master pedaling backwards, you will be able to slow down or stop a lot quicker than if you just used regular road brakes.
The ugly skeleton in fixed gear road riding's closet is getting something caught in between the chain and chain ring or cog. So obviously (1) do not wear loose clothing, (2) keep your shoe laces tied (and cut short and tucked in), (3) always wear shoes, and (4) keep fingers, important body parts, the family pet and of course grandmother away from the chain, chain ring and cog while they are moving.