Figuring out rendezvous and docking was one of the hardest things I ever did in KSP but I have it down to a science now. MechJeb is no longer needed. In fact, MechJeb is actually wasteful during docking because it spazzes out your RCS thrusters. So here's how to do it the "hard" way. A detailed guide to rendezvous and docking without using MechJeb and with visual aides.
Today this is the craft we are going to rendezvous with, named Agena in honor of the Gemini missions. I purposely put it in a highly inclined orbit for a wholesome demonstration.
Step 1: Launch Window
This is probably the most critical thing to the success of rendezvous and docking. It is possible to rendezvous with a ship that is 180 degrees out of phase (on the opposite side of the planet at any given point) but it is significantly harder and requires far more dV. So Launch Window - number 1. Its actually very simple on Kerbin. When your target is in LKO, the launch window is when the target strikes that India-like peninsula on the desert continent West of the KSC. Oh and make sure you launch IN THE SAME DIRECTION AS THE TARGET. I accidentally launched a craft into the proper plane but going the wrong direction on an Apollo style Duna mission that almost stranded my poor Kerbals.
Step 2: Launch Into an Orbit with a Similar Plane
Logical right? If your target is in polar orbit, you wouldn't launch into an equatorial orbit. That is what we call stupid. Of course, thanks to the inclination of my target combined with the rotation of Kerbin, rarely can we ever reach exactly the same plane so we'll just have to make it good enough.
Step 3: Match Orbital Planes with Target
This is the second most critical step to any rendezvous and docking, after the launch window. This will make it so your closest approaches to target are a lot closer. It makes the rest of this process a friggin breeze.
First, select the target in the orbital map and click "Set As Target." You will see its orbit turn green and a bunch of little bugs and dotted lines will pop up that you probably have no idea what they do. Not to fear. For this step you need only play attention to the green house-shaped bugs labelled "Ascending" and "Descending" Nodes. If you drew a line between these two points, it would be where the orbital planes of the target and your active ship cross. It is at these points you want to set a maneuver node to adjust your orbital plane because your orbital plane will rotate around the node.
Set the node at whichever you will reach first. Drag the purple triangles on the maneuver node adjust the plane. You will notice that your orbital will start to become elliptical. Not to worry; thats normal. Drag the Retrograde bug to compensate. It takes a little finagling because in your new plane, they are not mutually exclusive vectors. Eventually you will achieve a projected orbit that is at the same altitudes but an different inclination.
As you can see in the image, our projected orbit is within incalculable difference from the plane of the target because it reads NaN. Even 32 bit floating point can't see the difference. 
Step 4: Match Phase with the Target
This just means get pretty close. The thing is orbital mechanics are a little bit wonky at first glance. Even though I am behind my target, I have to burn Retrograde in order to catch up. If I was ahead of the target I would have to burn Prograde to fall back.
The explanation is boring and long so just believe me.
So you see those orange and purple bugs on the Orbit? Those show the location of the target and the active ship at their closest approaches. The best places in the orbit to phase match your target are at these points. Set a maneuver node at the nearest intersection.
Drag the retrograde / prograde vectors until the bugs are almost matched. Fine tune from there. You want your closest approaches to be within 1 kilometer. Typically these maneuvers don't take more than 50 m/s of dV, so be careful. You have to execute these burns precise to + - 0.05 m/s
Also be careful that you don't sink into the atmosphere. Looks like this phase match is going to be a two parter.
Yikes. 1.2 m/s! I should use RCS for this.
Well how about that. 100 meters at closest approach. That turned out better than I expected.
Step 5: Match Velocities at Closest Approach
Now that we are really freaking close to our target we can pretty much ignore the orbital map and just pay attention to the relative velocity indicator on the Navball. Once again, a long boring physics explanation involving inertial reference frames and relativity. Don't think you really are here for that.
Click on the velocity readout on the Navball until it goes to "Target" mode. This gives us our velocity relative to the target. When the closest approach rolls around, burn retrograde.
Burning. Burning. Burning
Excellent. We are separated by 600 meters on the day side. Lets warp over there.
Step 6: Docking
Your almost there. Remember earlier how I said we can pretty much ignore the orbital map now? All you need now are your eyes, some RCS thrusters, and the purple markings on your Navball. The circle means you are pointing directly at your target and the trefoil means you are pointing directly away. From here it really is as simple as pointing at your target and thrusting forward.
To use the RCS translation, switch to Docking mode down in the lower left corner. This will map WSAD to Forward, Backward, Left, Right respectively and Shift-Control to Up and Down respectively.
Weeeeee!
Oh yeah! Did I mention you can control your ship from the docking port? And set the docking port on the other ship as the target now? I didn't? Okay...
Did I also mention how easy it is to navigate? The RCS translation maps directly to the vector displayed on the navball. Thrusting Up moves the vector up, down moves it down, etc etc.
Almost there! When you get really close, magnets will activate and try to drag the two docking ports together. Turn off RCS and SAS for this and just let them do their thing.
Capture!
And there you have it ladies and gentleman; rendezvous and docking. Of course I am always looking for new insights so please comment, correct and help me improve.
