You can read about the general process of setting up a bass guitar in many places, so I will instead write about what works and particular problems you might encounter. These are things I've observed when learning to set up a classic 4-string P-Bass, and a modern 5-string dual-humbucker bass, both with roundwound and flat strings, so I think these points are generally applicable.
These tweaks made my grindy, cheap sealed tuners into smooth ones, without having to open them up (which isn't generally possible or worthwhile).
Before putting on strings, check that the screws and the main nut holding down the tuners are snug to the headstock and not too tight (don't crush the wood). Use a socket wrench or an adjustable wrench. Never use pliers. It will always damage the nut and if you slip, which is likely, the headstock finish also.
If present, tighten the tuner tension screw, usually at the end of the tuning peg. This keeps the internal worm screw tight against the tuner gear, reducing backlash and wobbliness.
Then, lubricate the tuner with WD-40 PTFE (Teflon) dry lubricant, or similar (an oil lubricant could leak out). Spray briefly a couple times down the side of the post (expect splashback, so covering with a towel helps) and spin the tuning peg around until the post has rotated fully a few times.
If a plastic nut is too soft, then the outer wraps of a roundwound string will impress themselves in the nut slot and cause the string to bind when tuning. The usual trick of painting the slot with graphite from a pencil won't help. A GrapthTech nut is the easiest replacement. They are pre-cut, so you just need to sand the bottom until the string height is correct. Sand on a flat sheet of sandpaper lying flat on a table so you don't get an uneven bottom surface. Adjust until there is a gap of about 0.003" (0.076mm), just enough for a scrap of paper to fit, between the first fret and the string when you press down at the third fret.
When gluing the nut, use as little glue as possible. Just the barest dot or two of superglue so it doesn't fall off when you change strings and so when you need to change it again, it will pop off with a couple taps and you won't have to scrape/sand off much residue.
When polishing frets, rather than tediously covering the whole fretboard with masking tape, make a quick guard with a slot cut out of a piece of posterboard or other thin non-corrugated cardboard, held together with a bit of masking tape.
I've found that a low neck relief, not a low action, is what makes a bass easiest to play. As measured at the 7th fret, with a capo on the first fret and a finger on the last fret, I aim for a bit under 1/64th of an inch (0.016" or 0.40mm), ending up closer to 0.010" (0.25mm).
You'll know it's time to re-adjust the truss rod when one of two things happen:
I've tried the extremes of setting action, but ultimately, the commonly given ranges work best: 3/64" or 4/64" (1.2mm to 1.6mm) at the G string, increasing to 5/64" or 6/64" (2.0mm to 2.4mm) at the E or B string. Too low an action makes fret buzz too likely. Too high an action makes the upper frets harder to play and limits how well you can set the intonation later.
Rather than adjust the action to your playing, adjust your playing to the action. Otherwise you can end up with setups which are artificially hard to play and limited in tone. The combination of the action height and the stiffness of your strings will affect where and how hard you pluck or pick on the strings. The closer to the neck you play, the lighter your playing must be to avoid clanking the string on the fret after the one you are fretting (though this is sometimes desirable as an articulation). If you want to play closer to the bridge, more flexible strings will feel better and sound fuller.
Generally, I find aiming for as soft a picking/plucking as you can gives the best results: less string movement means you can have lower relief and action, which makes fretting easier, which makes it easier to play softly, which means you don't need as much relief and action, and so on... Muting is easier since there is less sympathetic vibration of other strings. A light touch also means a richer tone as you don't have this overly loud fundamental and first few partials masking the higher partials which define tone.
Crank up the amp to compensate for a light touch. If you are worried about accidentally playing a loud note or clanking the string, then some very light compression either from a dedicated compressor, or even the naturally occurring compression of light overdrive, will soften that peak and allow you to rock out a bit, transforming that extra volume into extra harmonics instead, which is a useful articulation.
Having the strings closer to the pickup is better, giving more output and a brighter, well-defined tone as more partials will be picked-up. But too close will affect the motion of the string over the pickup, causing a warbling tone ("Stratitis"). Some pickups have massive magnetic pull (Jackson humbuckers), and some have comparatively almost no pull (Fender-Lace Sensors) while still having similar output levels, so I'm skeptical of the conventional string-to-pickup spacing of 1/8" (3.2mm) when pressing down on last fret.
A magnetic field near the poles of a magnet (or a pickup pole-piece) decays with the square of distance, so small adjustments have large effects. I solo each pickup, then play at the uppermost frets, first on the treble side, then on the bass side, and lower that side of the pickup very slightly (1/2 a turn at a time) until the warbling stops. Sometimes the bridge pickup can stay maximally high. Fender-Lace sensors have so little pull they cause no warbling and I have to lower them mainly so the strings don't hit them.
Having a low action means less displacement of the string when fretting, and less change in tension, so less compensation for intonation is needed as you move up the neck and more of the neck is usable before the intonation really goes off.
You can check the relative intonation of strings by playing octave chords (e.g.: 5th fret on E and 7th fret on D for an A octave). A good intonation setup will sound good across all strings up to about the 15th fret, and sound good all the way up the neck for the A, D, and G strings.
The inharmonicity of the thicker E and B strings limits how high they can play well with other strings, or even with themselves. Thinner strings will reduce inharmonicity, but I don't know how much that will help. Ultimately the tension gets too low, making playing with conventinal action impossible, and losing too many upper partials to get a well-defined tone.
Any electronic tuner is good enough for tuning to pitch, but for intonation adjustment a strobe tuner (e.g.: Peterson tuner or the TunerTime app) makes a noticeable difference. This is especially true for the B string, where minuscule adjustments have significant effect on a string that is already hard to keep in tune with the other strings.
A strobe tuner is so sensitive, you can see a string go off-pitch from the mere extra tension from string displacement while vibrating (another reason to play as lightly as possible), or changing the position of the bass guitar. Go slowly and be patient, and don't aim for an absolutely still readout (that's impossible), but one that changes slowly enough to enable you to see the effect of your adjustments. If your strobe tuner displays partials as well as the fundamental, then you will also see how a string become inharmonic as you go up the neck: the fundamental is in-tune, but its partials will go increasingly sharp.
That's it. Have fun.