Repairing & storing textiles
If the fabric itself has torn, then you have a fragile textile that probably is not strong enough to be worn. If the seams have given way, then it is likely that the original sewing thread is weak. Check all the seams, looking for broken stitches, loose threads, or similar weaknesses in the lines of sewing.
Resew where necessary, by hand, using a thread of a similar type and thickness if you can. The reason you need to do it by hand is that the seams will have lots of puncture holes from the original stitching, like the perforated edge of a postage stamp. If you re-machine sew, you will make even more holes and the seams end up even weaker that they were. In the worst case, the fabric will just tear away. If you had sew, however, you can stitch through the original holes, or make stitches longer (e.g. every other hole) to spread the strain.
In some cases tears are the result of accident, such as catching fabric on a nail or splinter. If this is the case, repair is possible but may not be invisible. Darning may be appropriate so long as it is done with care and skill. You will need the same or a finger weight of thread than was used to weave the original fabric. Matching the original colour is very important for a good result. Remember that darning must be worked over the weak or damaged area and into an area of strong fabric, or the repair will pull away and make the damage worse. Often, a more suitable repair method is to use a support fabric behind the tear, of a similar weight to the original, couch stitched into place.
The best way to store textiles is to lie them flat in a box or drawer. Limit folding as much as possible, but, where necessary, follow the lines already in place, for example seam lines in a costume. Use pads or sausages of acid-free tissue to soften folds and to support areas such as sleeves and shoulders.