What you tore off was the bumper cover. It attaches to the adjoining body panels with various types of retainer pins. Take any of those pins you can find and buy some new replacements at any parts store (NAPA has a better selection than your run of the mill Autozones/Advances/O'Reilly's), then use those to reattach the bumper cover. Each car maker has it's own type of retainer, so you'll need to match yours, they go by names like bumper push-pull pins, plastic rivets, etc. The parts counter clerk can help you get the right ones. If anything got torn like the foam padding underneath you'll have to reattach that too. The foam can be glued back together with a glue gun.
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