Things proceed in stages. Suppose the approaching vehicle is launched from the ground. The launch has to be very well timed or the rendezvous will not happen. For example, the Shuttle has a 2.5 to 10 minute long window during which the launch must occur if the Shuttle is to later successfully dock with the Space Station. Once on orbit, the approaching vehicle climbs, in stages, to close to the target vehicle's orbit. The goal here is to get close enough to the target vehicle so that sensors can see it, but not so close as to be a hazard. Up until this point, where the target vehicle will be involves a bit of guesswork.
Note that I said "will be". If you've ever gone duck hunting, you know what I mean. To hit the duck you need to aim at the spot where you think the duck will be when the shot crosses its path. Aim directly at the duck and you will miss. Don't take this analogy too far. A duck flies at about 20 m/s. The target vehicle is moving at about 7.7 km/s. The goal in duck hunting is a rather violent collision between the duck and the shot, and exactly where the contact occurs isn't all that important. The goal in rendezvous is a very gentle collision between the vehicles, and exactly where the contact occurs is extremely important.
So, now the two vehicles are about 20 kilometers apart. The approaching vehicle switches from absolute guidance to relative guidance. Relative guidance means the vehicle is using sensors to detect the relative position, velocity, orientation, and rotation of the target vehicle. The approaching vehicle slowly closes the gap between the vehicles down to a few kilometers and then a hundred meters or so. This is the near field rendezvous phase.
Those last hundred meters or so are very delicate. The last thing one wants is an uncontrolled collision. Closing the gap to ten meters or so is done slowly, often with stops. This is the proximity operations phase. How it proceeds depends a lot on how and where the final act of contact is to occur. Some vehicles dock directly with the target vehicle. Some reach a hold point and are grabbed by a robotic arm on the target vehicle. Others might grab the target vehicle with their own robotic arm. The vehicle can approach from behind, in front of, or below the target vehicle. The target vehicle can be cooperative or uncooperative. These decisions are made well before launch and often dictate the design of the approaching and target vehicles.
The final ten meters are the most delicate of all. A docking vehicle will close the final gap with relative speeds in the centimeters per second range. A vehicle that berths will simply stop (not so simply, actually; orbital mechanics can be cruel) and wait to be grappled.
