It does depend somewhat on what model of tent you have, but this should cover the basics:
1) Set aside the tent’s fly for the moment, and unfold and spread out the tent itself. Most dome tents are six sided (hexagonal), but bigger tents might be eight sided.
2) Assemble the poles. This just means unfold the pole and slide the pieces together. [Moderately important: later when you want to fold the poles up again, start in the center and fold in half, then fold in half each of the two halves, and continue by halves 'til you are done. This spreads the stress over the entire length of the interior shockcord. If you start at one end, part of the cord will be over-stretched, and won't last as long]
3) If the tent uses sleeves, slide the poles through the sleeves. If it only uses clips, skip to the next step.
4) Attach one end of each of the three poles (four for an octagonal tent) to a corner mount points. Lay the poles across the still-flat tent aiming towards the appropriate opposing corners (this will be automatic if you had to use sleeves).
5) Starting with the topmost pole (they overlap each other at the center of the dome), arch the pole until you can attach the opposite end. Ideally, have a helper hold it in place so it doesn’t pull the tent out of shape while you work on the others.
6) If this is an octagonal tent, the next pole should be the one at right-angles to the first. Continue with each of the other poles.
7) If some or all poles use sleeves, the tent will come into shape as you continue. If some use clips, you can hold off on attaching the clips until all the poles are in place. Then start with the clips at the center/top of the dome, and clip your way down alternate sides: you goal is to minimize the stress on the fabric of the tent.
Once the tent is up, unfold the fly. Figure out which side goes up (the zippers will provide the clue) and rotate it until the zipper for the fly matches that for the tent. Once it is lined up, clip the fly’s corners to the corners of the tent (how that works depends on the design; you might have to experiment).
9) Some dome tents have a short pole. This goes into fly and puts a kind of a beak over the tent’s doorway so rain runs down to the side instead of dripping down into the doorway.
Notes: one of the nice things about a free-standing tent is that they can be set up in one place and then picked up and moved elsewhere. So if you ever have to pitch a tent in the rain, find a dry-ish spot to set it up, then move it to the final spot.
Make sure you practice before you need to do this for real! Set it up in the backyard or a local park until it makes sense. If you might be setting it up after dark, get those head-band style flashlights so you have both hands free.