Orbital rendezvous is the process of matching orbits with another vessel. At the end of orbital rendezvous with a target, your vessel will be within a few hundred meters of the target and at rest with respect to it.
The Rendezvous Guidance module provides data that is useful for each step of orbital rendezvous. It can create maneuver nodes for each step, and optionally you can turn on an autopilot to do a fully automatic orbital rendezvous. Alternatively, you can just use the data and maneuver nodes and fly the rendezvous manually.
MechJeb performs orbital rendezvous in four steps:
Step 1: Align planes
The first step is to bring your orbit into the same plane as the target's orbits. That is, you need to bring angle between the two orbits--the "relative inclination"-- to zero. MechJeb will display the relative inclination; when this number is less than about 0.1 degrees you have relatively good alignment with your target's orbital plane.
Clicking "Align Planes" will create a maneuver node. Executing this maneuver should bring the relative inclination to zero. The burn is performed at either the ascending node or the descending node: that is, one of the two points where your current orbit passes through the orbital plane of the target.
If you aren't completely lined up after executing the maneuver node, just delete the maneuver node and repeat the process. Large plane changes may require several burns to properly align your orbit.
Step 2: Establish Phasing Orbit
The next step is to establish an orbit that is close to the target orbit, but of a slightly different size. Once you are in this "phasing orbit" you will orbit either slightly faster or slightly slower than the target, so that you will either catch up to it or let it catch up to you.
MechJeb displays the shape of the target's orbit in the form (perisapsis) x (apoapsis). It also displays your current orbit and a suggested circular phasing orbit.
Clicking "Establish Phasing Orbit" will create a sequence of maneuver nodes. Executing these nodes will bring you into the suggested phasing orbit. If you don't end up in the suggested orbit after executing the maneuvers, you can just repeat the process and try again.
It's not critical to achieve exactly the suggested phasing orbit. As long as your orbit is fairly circular and is close in size to the target orbit, you can move on to the next step.
Step 3: Hohmann transfer
The next step is to do a carefully timed burn that will put you on an intercept course for the target. Clicking "Intercept with Hohmann transfer" will create a maneuver node. This will either be a prograde burn that is timed so that you will intercept the target at apoapsis, or a retrograde burn that is timed so that you will intercept the target at periapsis. Note that this burn may be scheduled several orbits in the future: that is, you may have to go around your orbit several times until you read T-0 for the maneuver node.
Once you have executed the burn, delete the maneuver node and look at the values displayed by MechJeb for the predicted separation at closest approach. This is MechJeb's prediction for how close you will come to the target on your current trajectory. Ideally this will be within one kilometer. If you execute the burn precisely it will often be much less. If the predicted separation is too large, you can do little burns to try to decrease it, or you can use the Maneuver Planner function "fine tune closest approach to target."
Once the predicted separation at closest approach is small enough, you will wait until closest approach and then burn to match velocities with the target. Clicking "Match velocities at closest approach" will create a maneuver node for this burn in advance. After executing the maneuver node, you should be within a kilometer of the target, and your relative velocity to the target should be at most a few m/s.
If you don't end up near the target, go back to step 2, reestablish your phasing orbit, and then try again. If you end up near the target but with a large relative velocity, just kill your remaining relative velocity. To do this, put your navball in target-relative mode (by clicking the velocity readout until it says "target", if it doesn't already). Then point at the retrograde marker and burn until the velocity display reads 0 m/s, or close to it. You should end up at rest with respect to the target.
Step 4: Final Approach
Once you are with a few kilometers of your target and at rest with respect to it, the last step is to close the distance if you aren't already close enough. Clicking "Get closer" will create a maneuver node that will put you on a trajectory to slowly close with the target.
Once you have executed the maneuver and are on a closing trajectory, the final step is to match velocities again at closest approach. So go back to the step 3 tab and create a maneuver node to match velocities at closest approach. Once you execute this node, you should end up quite close (perhaps with a few meters) of your target, and your relative velocity should be less than 1 m/s. If you are still to far away, just repeat this process of closing and then matching velocities.
The rendezvous autopilot
Toggling "Autopilot enable" will engage an autopilot that will perform approximately this set of steps fully automatically. The autopilot will try to get you within 100 meters of the target and match velocities. Once it succeeds it will turn itself off.