Double-hung windows are made to be easily repairable without a whole lot of carpentry skills. If a window sash will not stay up, or is very heavy to lift, one possible cause is that the counterweights have detached from the sash.

This is a generalized description of how to rehang the counterweights in a typical double-hung window. Note that your actual window construction may differ from this description.

1. Utilize lead safe work practices (http://renovatedsm.com/node/176). Windows are a common source of lead paint dust - make sure you work safely.

2. Remove the interior stops - score paint with a utility knife, then pry with a thin pry bar or even a putty knife at each nail.
3. If the chains/ropes are still attached to the interior sash, pull the chain to give some slack and secure it at the pulley to prevent the weight from falling when you remove the sash. Use a pair of small vice grips or if it is a chain, you can push a nail through the chain to secure it. Do this on each side. (Obviously, if the chains have detached from the interior sash, this step doesn't apply). This will free up the interior sash.
4. Pull the sash out of the window frame and detach the chains/ropes from either side. Set the sash aside. This will free up access to the exterior sash.
5. This step applies if the weights have detached from the exterior sash as well. Pull out the parting stop (the long rectanglular piece of wood that separates the two sashes). You can probably use a pair of pliers - it's usually lightly tacked in with two or three nails. Be gentle but firm - don't break these pieces. Remove the exterior sash. Sometimes if the weights have fallen from the exterior sash, you or a previous owner may have screwed the exterior sash to the jamb to hold it in place. You will need to find these screws and remove them before you can remove the exterior sash.
6. Open the weight pockets. Sash weights in historic double hung windows are usually accessed in one of two ways: either through a small covered opening in the jamb (like this photo http://renovatedsm.com/node/246), or by removing the interior trim. Locate the weights.
7. Replicate the chains or ropes if required. Use the existing ones as a template.
8. Consider repairing the glazing or paint while the sash is out of the window. http://renovatedsm.com/node/462
9. Thread the new ropes/chains back through the pulleys. Secure the end of the new rope or chain so it doesn't fall all the way through the pulley while you are attaching it to the weights.
10. Attach them to the weights inside the weight pocket. I recommend using chain rather than rope. It's more expensive, but will last longer, and I think it's easier to work with.
11. Pull the chain so the weight is suspended at the top of the weight pocket. Release a couple inches. Secure it with the weight suspended at the top of the weight pocket.
12. Reattach the ropes or chains to the sash. You can use a small screw (don't screw it all the way through and break the glass) or possibly the original spring clip if it is still there, or a knot if it is a sash rope.
13. Replace the weight pocket covers sashes and stops in the reverse order you took them out.
14. Remove the nail or vice grips you used to secure the sash rope/chain. Gently lower the counterweight.

I may have forgotten a minor step in here, but it's pretty logical once you get going. Things to remember:

• Always secure the ropes or chains while you are working so they don't fall into the weight pockets

• Use the existing window parts as a template - replicate the sash cord knot, for example, if you replace the cords.
• Work carefully so as not to damage the stops or sashes.
• If you have the time and patience, it may also be beneficial to install weatherstripping or make other repairs while the sashes are out of the window.