Before setting the intonation, you may very well have to adjust the truss rod as well. The process should be to check where your bass is with the strings you know first. I'd measure the relief and the action, write them down, then restring and re-measure so you can adjust it to the same settings, at least as a starting point.
To measure action, measure the distance between the bottom of each string and the top of the 12th fret. I'd do this with the string fretted at the 1st fret just to make sure the nut is out of the equation. To measure the relief, measure between the bottom of the lowest string and the top of the 7th fret while fretting the string at the first and last fret at the same time. This makes the string function as a useable straight-edge.
Then, restring, push down on each string right were it comes off the saddle towards the nut (this creates a solid witness point for the string and helps prevent weird overtones, funny intonation issues, and eventual changes in settings). Now, first adjust the truss rod. Set the relief first because any changes to relief will change how your intonation needs to be set.
Then after the truss rod is right, adjust the string height at the saddles. Only then do you work on intonation. Roger's explanation of setting intonation is excellent. Remember that the idea is to compare the open string (and harmonics ARE divisions of the open string) to the fretted notes. It's more common to use the 12th fret harmonic instead to the 19th fret and there are good reasons why experienced set-up people differ on which to use.
The tempered scale used in most music (and for which fretted instruments' frets are positioned) does not align exactly with the harmonic created at the 7th and 19th fret. That's why I prefer to use the both the 7th fret and the 12th fret and average the results. I also suggest using a GOOD tuner (and that's pretty much in my experience a real strobe tuner or the Peterson virtual strobes- the standard quartz timing mechanism used by almost every other tuner is woefully inaccurate for precise intonation setting). And, make your assessments with the bass in playing position. Many basses' necks will flex if you have them on a table while working on this, and that flex can be enough to create a noticeable difference when you wind up playing in the real world.
After you get the set-up done, play it and listen carefully for balance across all the strings. Adjust the PUPs to even them out if needed. One good way is to simply pluck each string hard (like the snap part of slap/pop). That gives a pretty consistent attack for most people. I used to use an old compressor I had with an analog VU meter, but that was back in my really anal days. I've since found that my ears are just as good...