Honestly, the best approach depends on what the piece is made of and whether it still has life left. Start by giving it a quick safety check: loose bolts, rust, cracked plastic, splintered wood, broken glass. If it is fixable, repair it or pass it to a neighbor who can. A lot of old outdoor furniture just needs a clean, a coat of paint, or replacement screws. If you are not keeping it, take clear photos and list it on Buy Nothing, Nextdoor, Freecycle, or Facebook Marketplace as free or cheap, and be upfront about any faults. Local charities, community gardens, shelters, and furniture reuse groups may take sturdy benches, tables, or chairs, but call first because they often have pickup rules.
If no one wants it, check your city's waste rules before putting anything at the curb. Many cities offer bulky waste pickup by appointment, or have drop-off recycling centers for metal, plastic, and wood. Search for your city's bulky item pickup and recycling center rules, and ask specifically whether they accept treated wood, cushions, glass table tops, and mixed materials, because rules vary. Metal frames are usually recyclable; plastic resin furniture may or may not be. Cushions and fabric often go in general waste unless a textile recycler takes them.
If you are allowed to disassemble it, do it safely: wear gloves and eye protection, bag screws and small parts, tape sharp edges, and separate metal, plastic, wood, and glass. Do not burn painted or treated wood, and do not leave it in an alley or park, since that can count as illegal dumping. If you cannot transport it, book a licensed bulky waste service or ask a neighbor with a van. For public or shared outdoor furniture, contact the property manager or city parks department rather than moving it yourself. The goal is simple: reuse first, recycle second, and only then dispose of it through the proper city channel.