On your new BB, one side will pull right off and the other side is pretty much permanently attached.

Screw the side that pulled off into your bike (make sure you're putting it into the correct side of your bike by noting L/R markings on BB body.) If it's the right side (AKA drive side) it will screw in counter clockwise. Don't tighten it down, just get it most of the way in.

Then insert the rest of the BB and tighten.

Then go back to the first bit you put in and tighten it.

There are probably videos that show this being done on Youtube.