Depending on your choice at the end of Architect's Plans, you will have the choice of one of two approaches to this mission. If you choose the Fire Crew approach, you need to have set a getaway vehicle, as well as finish Fire Truck. The other approach, Roof Entry doesn't require any extra missions.
Both walkthroughs will take into account you hiring the best people for your crew (usually the ones with the highest cuts).
Get into your vehicle and head to the FIB building, entering it and going to the turnstile once inside. Head to the elevator and after reaching the designated floor, go to the maintenance closet to grab the mop and bucket. What you have to do here is go to the dirty spots on the floor, mop a single time, go back to rinse your mop and do the same for the next spot.
If you try to clean more than one spot without cleaning the mop in between, you will smear dirt on the floor and have more work to do. After finishing the first area, plant the bomb and go to the next room. There are more spots here, but it's the same thing. Plant the bomb in the bathroom after you're finished, then bring the bucket and mop back to the maintenance closet.
Exit the building and go to the marker, where the game will switch to Franklin. Pick up Michael and then set off the charges, driving to the front of the FIB building. Head inside and ride the elevator up, following the others to the stairwell to get to the top floor.
Note the oxygen meter, which indicates how much you have before you will suffocate, but that shouldn't be a problem at all, as you have plenty of time. Follow the corridors around until you get to the room with the containment drive, which needs to be blown open since the door is locked. Grab the drive and then follow Michael.
Keep following Michael, past the door that gets blasted open by the fire, until Franklin ends up passing out a bit. Get out a gun, as you'll be separated from your crew and there will be some agents in the way back to them. There aren't too many, and the tight corridors make for a lot of cover. The last one will be in the stairwell, then you can meet back up with the crew.
Climb up the rubble and continue following everyone to the elevator shaft, where you will need to rappel down to get to the ground floor. Exit the building and get into the Firetruck, driving to the getaway vehicle. When you get there, plant a Sticky Bomb onto the Firetruck and when your crew is clear, blow it up. Drive to Lester's place now to finish the mission.