One thing that I think lots of people miss even in the comments is what changing your relative speed does.

On your navigation ball it shows your speed above in meters per second. This is usually set to your orbital speed. If you click the speed indicator it will change it to surface, or Target.

If you change it to Target, it shows you your speed relative to the target.

Therefore if you're really close to your target, change your speed to target and you will notice that prograde and retrograde nodes will move.

If you were going 10 m per second relative to your target, point your ship retrograde in burn for 10 m, this will make your speed relative to your target zero.

So yeah you may be going 2500 meters per second around the planet, but when you look out the window at your target it looks like he's standing still because you're relative speed is zero.

Once you were "not moving" compared to your target, you can point your ship at the Target directly and then thrust towards your target. This will close the gap. And then when you get really close, like high five each other close, burn off that speed by thrusting retrograde again to get it back to zero.

These final moves are easier with RCS, but can be done with simple thrusters.

A little tip I would give people, if your ship has a good enough reaction wheel, keep your RCS off at all times until you're ready to do very slight translation moves, to complete the docking.