What's the best way to seal up leaky old window drafts?

I would use the foam you put around pipes with some white duck tape, works great.

Duct tape thick clear plastic over the entire window and any gaps around it.

Use the plastic window kits available at hardware stores, Walmart , and homecenters.

Hi Carol. I'm Cindy. My neighbor has very old windows in her home. She has been in her house 44 years with no changes in all that time. This is the time of year that her sons come and winterize her house. They do a bunch of stuff and one of those things is with her old windows. They put up those sheets of plastic and blows them with her blow drier. They conform to the shape of her windows and seals off any drafts. I believe that 3M makes this kit. I hope this info helps you. Best wishes and good luck.

Caulk first.

If you're paying the heating bill, try convincing your landloard to caulk the windows. You could then purchase or sew heavy lined draperies.

Sew, knit, or crochet your own draft stoppers.

If it is a temporary seal you are seeking around windows, Home Depot, and others may carry a product with the calk called Seal-n-Peel. It goes on like caulk, and after it cures you can pull it off in one piece when you are ready. We use it around our window air cond. in the summer to prevent bugs from sneeking in, and around windows that will be shut during winter.

Tub & Tile peel & stick vinyl tape has a fold set in it for going around tubs. May sure window is dry when you apply, but this works good for rental units. When you leave, just peel it off.

These are the kits mentioned above.