Please supply a floor plan so that we can see what it is that you are dealing with.

Hopefully this is legible enough....the previous owners of the house never supplied floor plans.

If no one else uses the space IMO I would just leave it alone he or she will have enogh privacy and a good set of headphones will address the noise proofing . Put the bed in the space furthest from the stairs and be done.

Do you need to keep the sound IN our OUT of the basement? Headphones might be a good option. :)

This might actually be one of the very few places where barn doors make sense.

Neither heavy curtains nor barn doors are particularly soundproof. Wireless headphones + curtain may be a cost-effective alternative.

Google "portiere" for ideas of curtains for doorways.

If you want a temporary solution before you can get a pro:

The least expensive -- and least permanent -- option for if no one in your family is particularly DIY inclined would be to hang a sturdy double curtain rod over the opening on the basement side of the opening and use a "curtain" you create as a fabric wall. Measure the width of the opening so you know what length double rod to get.

Stitching rings (think curtain or even shower curtain rings) to quilts or comforters or blankets you already have so they can be hung on the rod. This would begin to provide privacy and some sound barrier, albeit not as much as a solid wall with a door or with French doors or with a sliding glass patio door.

You should be able to get a double curtain rod and rings at WalMart and, with a ladder (or stool or chair) and a screwdriver, you and your teen should be able to hang your rod yourself. Check to see which kind of screwdriver you'll need as you buy the rod and brackets. Hang the brackets for the rods where you know there is framing behind the drywall. There will be a wood frame just above the opening and a wood plate just beneath the ceiling .

In the meantime, check with your local Home Depot and see if they will be resuming classes on home building projects and see if your teen, male or female, can attend.

Check out the DIY magazines at your closest Lowes or Home Depo and see if they have one on how to build a wall.

Also browse through the magazines for potential permanent barriers -- sliding glass doors, French doors, wall across part of the opening with a centered standard interior door. You could then make an informed decision when you are able to talk with a pro or decide to use this as a DIY project.

If you don't have a truck or a vehicle in which you can carry the materials needed, you could have them delivered. Delivery cost might be less expensive if you have their favored credit card -- ask.