'm familiar with working with lead, much less so for asbestos. I did get my lead safe certification this year at the individual employee level, so I can run a lead site but am not certified to own the lead program or most importantly do any sort of legally mandated abatement work. This is from the MA state course and some refs vary a bit state to state but this should be a good starting point:
For lead, we're taught if the house is older than 1978, operate under the assumption you're dealing with lead paint. That was when the big lead paint law drew the line in the sand.
Working with any hazardous construction material, the danger from least to most goes: flakes, dust, vapor. If you're cutting out a whole wall of drywall, your sawzall will create the dust. Not a ton, but as a precaution, you can spray the wall ahead of your cut. The wet dust won't suspend in the air floating and being a hazard.
For PPE, the bare minimum is respirator, safety glasses, and covering any open cuts. I'd recommend a tyvek suit, but if you can't/wont buy one, just make sure you wash your clothes by themselves as soon as you're done.
Put plastic sheeting out on the floor 3' from where you'll be disturbing the hazard. For a whole wall, I'd probably just sheet the whole floor. Also hang 2 sheets of plastic from the door jamb to make a little curtain to discourage airflow between clean and dirty spaces. Make absolutely certain any vent is well covered.
For cleanup, wrap up all the sheeting in a tamale looking blob and duct tape around the middle. This can go in the regular garbage. Swifter wet wipes work well, wipe down surfaces until you're not getting a dirty pad. There's a specific spec, I think I remember it being 10x10 that has to get 2 passes without discoloration.
If you're in a place by yourself that should be more than enough. If there are kids living in the space, so more anal on the cleanup, as their brains are more at risk.
