The basics of clearing a house ... ? That would take up a medium sized book. And it really and truly cannot be learned on paper; you have to learn it by doing it, over and over again, until you can, at least sometimes, get it right.
There's a reason everyone tells you not to do it!
Nevertheless. If your master bedroom is downstairs and your children sleep upstairs, you may have Darn Good Reason to check out the bump in the night. I for one have no intention of leaving my children in harm's way while I huddle in the safe room, and I cannot just set up shop at the top of the stairwell because the floor plan of my house isn't exactly conducive to that. (But what I'll do is race to where they are, cautiously but quickly. I won't do a full search, just glance and go. This is not clearing a house ... and it is stupid, just less stupid than hiding in safety while my loved ones may be at risk. That's the choice I've made.)
But maybe your situation means that you really and truly have to really search. So here's a quick overview. Again, don't do this if you have any reasonable alternative.
Important base concept: Slice the Pie. Just as you probably would not sit down to eat an entire pie in one huge indigestible mass, you cannot search an entire house all at once. If you break the pie into smaller pieces, and then break each piece into bite-size portions, the pie is more manageable ... and so is your house. From where you are standing, check everything you can see. Check slowly, and check again. Any time you get overwhelmed with the size or danger of the job you just took on, break it down into a smaller piece, something that isn't so overwhelming. Do one thing at a time, one area at a time.
So there you are, standing there. Looking.
What are you looking for? Pieces of people. You aren't looking for an entire human being. You're looking for a flash of color where it shouldn't be that color. You're looking for someone's oversized tennis shoe sticking out from under the drapes. You're looking for a sliver of someone's elbow.
You're also looking for danger points. If the room you are in is clear, your danger points are the entryways into that room -- the window(s) and doorway(s). Those are the spots to watch. If you don't yet know the room is clear, your danger points are anywhere an attacker might be hiding: the closet, the other side of the bed where you cannot see the floor, behind the wardrobe, behind the open door. You must watch all of the danger spots, every time you move. As you move, old danger spots will close off and new ones will open up to you; be aware of this and keep watching the new ones.
You're using all your senses. Smell the air. Does it smell like someone's been smoking in your non-smoking home? That's what we call A Clue that someone might be in the room with you. Listen! Do you hear anything at all? A shuffled foot, a faint breath, anything? What direction did the sound come from?
You still haven't moved, have you? Good. When you move, you're going to move quietly. But not yet. First you're going to equalize the environment. If you're in the light and the next room is dark, you are at a disadvantage, because you'll be very visible to an attacker who isn't as visible. Equalize by either turning all the lights off, or all the lights on. Don't get silhouetted in the doorway, or a window, or anywhere else.
Okay, now it's time to move. Don't move your feet yet. Start with your eyeball. Your eyeball is going to lead you around corners -- not your feet, not your hands, not the gun. Your eyeball goes first. Tilt your head and blade your body to the nearest, biggest, worst danger point so that your eyeball leads. Lean out slightly and look at everything there, floor to ceiling.
If there are other danger spots (there will be), look at them too. Then and only then, take one small step toward the danger point you just checked. Stop and listen. Keep using your eyes and your nose. Lean slightly and check everything again.
Does this sound slow? It is. Clearing a house takes just about forever.
Keep your back to a wall if you can. This cuts your danger from 360 degrees down to 180 degrees.
Remember where the mirrors are in your house. It'd be embarrassing to shoot one. (And more embarrassing to be killed by a BG who was watching your every action in one...)
Stay behind cover as much as you can, or behind concealment. (A standard indoor wall is not cover -- it won't stop a bullet. It's concealment.) Concealment is better than standing in the open.
Never ever ever expose your body to an area you haven't yet cleared.
Don't stop in doorways. See as much of the room as you can by slicing the pie first one direction, then the other direction. Then choose a specific place in the room you're going to move to -- someplace you know is safe. When you move into the room, go very very quickly. Get your back to a wall, and keep your eye on the part of the room you haven't yet seen.
Don't get outlined by a window. Remember BGs can be outside the house looking in -- or climbing in.
Human beings can fit into incredibly small spaces. Remember this well.
Don't forget to look up high. Many predators like to hunt from a high spot, because prey rarely looks up.
If you see something out of place, something you know for sure means a BG is in your home, leave if you can. Don't go into denial. Don't keep looking for more evidence. Just grab your loved ones and go. There is nothing in the house worth your life.
If you use a "quick peek" around a corner or into a closet ... and spot a BG ...don't go back! At that point, the search is over. You can stand behind cover or concealment and command him out, or you can leave the house to him and call the cops. What you cannot and should not do is go back in after he's seen you, because then he has the advantage.
If you spot a BG, but the BG hasn't yet seen you, remember you can leave. You do not have to engage him unless you desire to do so. If you do engage him, if you are inside your own home, in most jurisdictions you do not have to give a verbal warning. Remember you can give a verbal warning or command if you wish.
If you do verbally engage the BG, don't be a wuss about it. "DON'T MOVE!" explosively shouted from the diaphragm, is a pretty good opening line. "Um ...eerrrrr, excuse me, what are you doing in my house...?" is not quite as good.
BGs have friends too. If you spot a lone BG, remember this ... and don't get caught by tunnel vision.
When you think you have the basics of searching down pat, play hide-n-seek with a 10 year old who's armed with a rubber band gun ... or with a buddy who's carrying an Airsoft.
pax