Long Ship Physics Problems

There are several steps to successful dockings. Click on images for larger view.

1. Set your target as your target.
2. Time your launch: A general rule of thumb is to launch when your target is just rising in the west (unless your target is in a retrograde orbit). If your target isn't in an equatorial orbit, then you'll also want to launch when the orbital plane crosses your launch site.
3. Launching: this is pretty standard. One key thing to remember is to set your apoapsis to meet your target altitude. Circularize as per the next step.
4. Closing the gap: if you're leading your target (in front of it), you'll want to increase your orbital period. Burn prograde to increase your apoapsis about 5km higher than your target, or until the intercept minimizes. In a similar vein, if you're trailing your target, you'll want to decrease your orbital period by lowering your periapsis. Also take this time to make your orbits co-planar by burning in the normal or anti normal direction at the descending or ascending node respectively. If you're already within about 5km, you can skip this step.
5. Initial approach: by now, the nav ball should be in target mode. In this mode, your velocity vectors indicate the relative velocity between you an your target. Keep your prograde vector pointed at the target, and reduce your relative velocity to under 50m/s. As you close in, continue making adjustments to your course to keep your velocity vector on the target indicator and continue reducing your relative velocity.
6. Final approach: by the time you're within about 1km, you should have a relative velocity less than 10m/s. Hopefully you remembered to orient your target ship such that one of the ports is pointing north or south (for equatorial orbits, normal or anti normal in general). Point yourself in the opposite direction, thus making the axis of the two docking ports parallel. Now you can switch to docking mode, as you don't want to use your main engine anymore. Change your view to Chase by hitting V a few times. Now use translation controls to line up the axis of your docking ports, thrust forward, and let the docking ports magnetism do the rest. Just not too fast. Keep it under 1m/s within 10m.

As a side note, I screwed up this particular approach because I wasn't paying attention and didn't reduce my speed as I closed in. I shot past the target ship and had to correct. Additionally, you'll note that I didn't in fact change to docking mode. This is a personal preference, and I use both hands on the keyboard to control my attitude with my left had (WASDQE) and translation with my right hand (IJKLHN).

There is no stock way, as of 0.23 to save which or how many Kerbals are assigned to each mission.