Install a solid core door. Make sure that it is heavy and solid and fits the door frame as exactly as possible.
Install soundproof windows over your basement windows. Since your windows are the thinnest part of your basement wall, adding another layer of windows on top of them is one of the best things you can do to sound proof.
Find the studs in the wall. Use a stud finder and mark the location. You should find another stud either 16" or 24" to either side, and another one after that. Mark the location of studs using a pencil mark or a piece of tape at the baseboard.
Measure and cut sheets of drywall to the desired size.
Using a caulk gun, apply a layer of green glue to the sheet of drywall. The covering should be uniform, but it does not have to be smeared out and leveled along the drywall. When it is compressed against your existing wall, the glue will compress and spread.
Push the sheet of drywall against your wall.
Using drywall screws, anchor it to your wall along the studs. You should screw it in about every 8 inches along the wall.
Fill the drywall joints with a layer of joint compound.
Install heavy, thick carpets with thick carpet pads in the rooms above. This is easier and cheaper than soundproofing the ceiling from below, and will help to stifle sound.