Hodari

Right click on the docking port of your ship and select "control from here".  Right click on the port on the other ship and "Set as target".  Turn your ship so it is pointing towards the target.
If you can, switch control to the other ship and do the same from there.  Now your docking ports will be facing towards each other and it will be much easier to do your final approach.
Then just use RCS to VERY slowly(When I'm this close, I usually keep it to about 0.2m/s) approach and also make sure you keep the target and prograde markers aligned and keep your ship pointing toward them.

That's more or less correct.  To add a couple more very important details though:
1.  Review the contract very carefully.  Especially pay attention to which direction the orbit is supposed to be going in and to what parts the satellite needs to have.  You don't want to get it up there and then find out you're orbiting backwards or that you're missing one of the parts.
2.  If the orbit is inclined at all, you'll want to wait until the KSC is directly underneath it before you launch.
3.  Try to launch as close as possible to the required inclination so you don't have to do a huge burn later to fix this.
4.  Get into orbit.
5.  If you do need to correct your inclination at all, do so at either the ascending or descending node.
6.  Match the periapsis and apoapsis.