in the removal section there is a list of things to take, and some pretty detailed descriptions of cutouts. lots of pictures also.
i'm sure everyone does it differently and what you find will make some difference. i'll tell you what i do, but there are masters on here and i am just a grasshopper :-).
take the time to set up your equipment. make sure your hive is ready, lay down your tarp, make sure all your tools are handy.
the first thing i do when i take off a wall section like that is look at the piece i have removed. often comb is stuck to it and a couple of times i have found the queen there. it's important to remove this piece gently if you can. don't just toss it aside.
when you look at the hive, the comb will probably be vertical and between studs. often the outside comb will be empty. it may be full of honey. i use a sturdy paint scraper to pry this loose. honey goes in the honey bucket. empty comb goes in the comb bucket or on the tarp. the center combs will have the bees, brood, and probably queen. using that same scraper, or a clean one if the 1st is really gunky, i just gently grasp the comb and cut it loose. if it's brood, it gets banded into frames and set in hive. if it's not brood, i set it beside the hive, or even on the top if i'm almost done so the bees will be able to go in easily. if you can find the queen and get her into the hive, the bees will start settling in. if you don't see her, don't worry. she's probably on that brood somewhere.
a bee brush and dust pan are handy to sweep up the bees that don't want to co-operate.
it's pretty messy. you'll end up taking a bath in honey and you'll kill a lot of bees. the first time is hard. after that, you realize it's not so different than an inspection in your own hive, except you have to handle them more.
i think the most important thing is to take your time and be methodical. try to have a bit of a mental plan before you start. read through the removal section and the equipment sticky.
one more thing. twice in outbuildings i have found that the hive became two. now i always take an extra super setup. don't forget the straps or staples.