The ultimate purpose of a lead out is to dump you in the lead with 150-200m to go in a flat sprint. Ideally, the pack is strung out and there should only be several riders within striking range to challenge the sprinter. A good sprinter is able to accelerate to the line from that distance and should be able to hold off the other with the 1+ bike length lead.
A traditional lead out has several components and should ideally have more than 1 rider in the "train". One main purpose of lead outs is to keep the sprinter sheltered and to keep breakaways from succeeding. This requires the leadout rider to ride at a fast pace to discourage attacks and to string out the peloton. It should not be so fast as to shell the sprinter. Stringing out the peloton also keeps the sprinter from being boxed in, helps prevent crashes, and makes it very difficult for your opponents to move up. The best riders for this role are strong riders who can ride fast for a long time but they might not have the best sprint or short duration speed.
As the race gets close to the finish, the actual "leadout sprint" is ideally conducted by a good sprinter who will deliver you to about 150-200m from the finish. This rider should engage from around 1000m to 400m (the distance depending on the strength of the rider, course, and race conditions) from the finish in what is pretty close to a full on sprint. One of the worst things a lead out can do is to jump too early or too late. If the leadout goes too late, you will probably get enveloped from behind and get boxed in. If the lead out goes too early and dies, it will leave you hitting the front too far from the line. Beating other good sprinters from the front at 400m out is pretty much impossible unless you have a name like Cipollini.
If you look at the pro teams, a lead out train will consist of 4+ riders and the train will start at a distance determined by the number of riders available. As the finish approaches, the lead out gets faster and faster and riders will ride at the front and peel off completely spent. If done well, the lead out train keeps other teams from organizing their own train and is perfectly timed so that the sprinter is given an arm chair ride to the finish. Sometimes there's even a "sweeper", a rider who is assigned to sit on the wheel of the sprinter and keep other sprinters from coming off his wheel. In that way, the other riders would then have to make up a 2 bike length lead once the sprint is engaged. In professional racing, the best counter to a lead out train is a competing train. In the US, I would say the best lead out trains were executed by Healthnet and Colavita. In Europe, it was hands down Fasso Bortolo.
If you only have one team mate, I would say that his job is to keep you out of the wind and to move you up close to the front before the finish. He should do all the dirty work of chasing down the attacks and perhaps he might me able to jump before the finish and drag you to within striking range of the finish line. The key is to communicate well before the race and also during the finale. Organized team work is really difficult in a sprint: sometimes you just have to be willing to abandon your plans and go from wheel to wheel. Of course, it's the small things that can sometimes make a difference. Even if you can't get a lead out to work properly, a team mate can let you in near the front if you're dropping back, or perhaps they can attack if you are boxed in so that the reaction can free up space for you to break free. Of course there's nothing like shouting "go, go, go!" and then having your team mate screaming into the last corner of a crit with you on the wheel...