If the stems are still alive I'd trim off the dead foliage and any stems that are questionable then water it well. You might want to set in in a tray with a few inches of water and let it draw it up through the bottom so the soil gets saturated. Remove it from the tray after an hour or so depending on how big of a pot it's in. A small pot won't take that long to "drink" and a large one might take longer. I hope you are able to salvage your jasmine.
Karyn