I reverse duct tape on a paint roller, screw it on a broom handle, and roll away. When it's no longer sticky just replace the tape.
You can either dry mop it or use a vacuum cleaner. If it is really dark then you may need to paint it. First, put a good quality primer on it such as Zinsser Bullseye 1-2-3 and then a cost of Ceiling paint. Ceiling paint products are tinted either pink or blue so that you can see where you are painting and they are thick so that they do not drip. If you decide to paint, be sure to select the correct roller for textured ceilings.
Unfortunately there isn't any it would crumble off. In a newer home that ceiling has not been previously painted you first use a latex ceiling paint then paint again with regular wall paint otherwise it will crumble off. They will give you advice at paint store as paints change.
I use my vacuum with the floor attachment. The soft bristles reduces the amount of popcorn that comes off, even though it's inevitable you'll have some cleanup.
Doesn't the popcorn that comes off not clog your vacuum? I've got a Dyson but I didn't want to ruin it on the ceiling. I'm trying to prepare for a new paint job but have no desire to paint dirt also.
No. Not that much actually comes off. You don't have to have your attachment in full contact. If your vacuum has good power, you basically can just have it barely touching. Just make sure to empty the canister where the dirt goes into, and make sure your filter is clean.