Seeing a lot of discussion, but not much real information here, so I'll contribute.
For starters, here is the website: https://lasers.llnl.gov/
And here is a page of that site that has some explanation about how it works:
I've actually toured this facility, and it was pretty damn cool. A few points that stuck in my memory:
The generally do one shot each night. They prep it during the day, then they all go home and it goes off at night with not many people there, because that's safer.
The electricity usage is intense but very short, lasting only around 20 billionths of a second. They do this by charging up their capacitors and then discharging them very rapidly. They said the air conditioning for the building actually uses more power than the laser.
They talk about the "seven wonders of NIF", which are seven advances in materials and technology that were made during the project which made it all possible. I thought the rapid crystal growing was pretty wicked. Info on them here: https://lasers.llnl.gov/about/nif/seven_wonders.php
In the actual ignition step itself, while you might think you shine the powerful laser on the thing you want to heat up, that's actually not how it works. They have the thing they want to heat, and near it (like 1mm) is this little metallic trough thing. They blast the laser into the trough thing and when the light hits that it creates microwaves, and the microwaves heat the target. Of course by the time it's done all those parts are completely vaporized.
Also of interest, around April this year the place was shut down for maintenance for a month. For about two weeks during that period some filming for the next Star Trek movie took place inside the NIF facility. So check out the pix and see if you can spot the NIF scenes when the movie comes out. It does kinda look like the engine room of a starship: https://lasers.llnl.gov/multimedia/photo_gallery/target_area/?id=5&category=target_area
Obviously, the whole lab is full of nerds who like Star Trek, but they were not allowed to see what was going on.