Hi Mary, the best way to re attach the mesh under your furniture is usually with a staple gun. You can pull it taught and then staple it to the wood frame of your furniture.
If this were my furniture I would just remove it. Pulling it taut, would probably just rip it more
Mary....You can purchase at a fabric shop the amount of material you need to replace the torn netting. Remove it and staples that are holding, use the netting you removed to cut the new, fold down edges and staple one side, go to opposite side pulling taut and staple then to the other two sides. Good luck
They sell that type of fabric at most fabric stores, purchase it a little wider than you need then fold it under and staple to the bottom of the chair frame.
Did it completely come off or tear?
This tutorial might help: https://www.youtube.com/watch?v=DgpS-Tnb_18