From what I've seen, it looks very tricky. I have yet to do it. But like most things in X3, once you get the hang of it, it can become fairly easy.
You have to be flying a ship (personally, not remotely, I believe) that can carry marines. When you are correctly positioned so the target ship will run over your marines, you give them orders to board and they jump ship and latch on. But first you have to take down the shields of the ship to be boarded and keep them down until the marines cut their way in. You can also make marines use boarding pods if your ship allows, which increases the chance of entry, and appears easier than spacewalking marines.
Each marine can be trained in 4 stats - fighting, hacking, mechanical, engineering. These stats affect fighting once inside, hacking to gain control, chance of entry, and minimizing collateral damage to the ship. Only the last 3 can be trained in stations. Fighting is only trained by doing boardings. You can lose marines during a boarding, too.
Quite a few kinds of ships can only be obtained by boarding. For example, the Hyperion Vanguard is regarded as the best M6 by many (or at least a close second to the Springblossom), but can't be bought, doesn't bail, but can be boarded. Khaak, Xenon, and Pirate capitals cannot be bought, don't bail, but can be boarded. Same thing for the some of the ATF ships.
Once you have a PHQ, you can reverse engineer some of these (and other unique reward) un-buyable ships from the example ship in your possession, and then build copies of them for your fleet.
It's another of level of gameplay I definitely haven't touched.
PS. To answer your FPS question... Boarding happens separately while you remain piloting the ship. You get a running audio commentary as the boarding progresses, and you can apparently monitor what each marine is doing via the property window. Yes, marines are treated as property. :/
