It depends on your slingshot. First of all, make sure you get the right band for your particular slingshot.
Most replacements are pretty self-explanatory but replacing tubular bands that feed over uprights can be tricky. For these, use a sharp knife to cut the old band off, then use rubbing alcohol as a lubricant while you feed the new bands over the uprights. Wait for the alcohol to evaporate, and you’re good to go.