Permanent fix for leaky window/door frames
Short of replacing leaky windows, the simplest permanent fix is to insulate between the window frame and the framing of the window's rough opening and coulk the molding well. Most windows and doors that I've removed that were installed prior to the 80's were not insulated AT ALL... Even if you have had them replaced within the last 10 or 20 years it is possible that the contractor took a few shortcuts and never insulated. You can try this on one window or door to see if there is currently insulation installed. If one is missing it, chances are all of the windows in your house are. This should be fairly easy and maybe even a fun reason to make a small mess and use some tools for any entry level do-it-yourself-er.
1. Remove window moldings
Carefully run a sharp utility knife around the outside and inside edges of the window or door moldings. This is to separate and paint and/or caulk that may be holding the casing to the window or to the wall. Use a hammer and a small, sharp prybar to remove the moldings from the window and wall. Go VERY easy here so that you do not crack the moldings. Unless you are in the mood to spend a few extra bucks and replace or upgrade your moldings and paint, you will be reusing them.
2. Insulate the gap between the window/door and the rough opening
Using a sharp utility knife, cut lengths of fiberglass insulation (any type such as R-13, R-19, etc.) to lengths approximately the size of your windows, usually 3 to 5 feet long. Cut these pieces into strips about 2 inches wide. Now you can use your hands (and I would advise using gloves to keep down the itch factor) to tear the 2 inch rips down to size depending on the size of the gap you have to fill. You want the insulation the be only slightly wider then your gap (see below). Using a putty knife or narrow spackle knife, stuff the insulation into ANY and ALL gaps that you can reach retween the window frame and the rough framing of the house. DO NOT PACK TOO TIGHTLY.
It is possible to over-insulate. If you pack too tightly you will actually lower the R-value (insulation value) and the insulation will become a conductor instead of an insulator. For best results the insulation should be pushed in far enough that it is in line with the window panes or door panel.
3. Re-install moldings
Using a hammer and 4 or 6 penny finish nails, carefully reinstall the old trim in its previous locations.
Clear or matching color silicone works best but any sealant that remains soft and pliable after it's dry will do. Caulk the moldings both to the wall and to the window/door. Although your rough opening is now well insulated, it is still possible that there is a hole or uninsulated cavity elsewhere in the wall and any air that enters that location can find its way to your window opening. This will stop any blowing air that has reached the opening from entering the home.
Temporary (dead-of-winter) fix
Many older windows are made with only single pane glass, which readily allows transfer of hot/cold air by conduction. To slow this transfer of temperature, you must create a buffer zone between the outside and inside temperatures.
To do this you can quickly and easily install a plastic film over the window. Thickness of the film is not important. The thinner the film (something like a wide saran wrap) the less noticeable it will be. Simply stretch the film over the opening (on the inside) from molding to molding and continuously tape with a removable painters tape directly to the molding. If you suspect air is entering around the outside of the window's frame, tape the film to the wall itself (or see above 'permanent fix').
The air between the film and the window pane is now a neutral zone and will dramatically slow the cold air from outside from eating up your expensive heated air inside.
NOTE: the window will be inoperable while film is installed.
NEVER caulk a window sash closed. Windows are and egress point in case of fire and should always be kept operable.