The short answer is to give the wind fewer chances to get underneath your furniture, and connect the furniture to something heavier than the wind. I live with a small city balcony, and I learned this the hard way after a lightweight side table took a trip across the patio.
Start by choosing the most sheltered spot you can. In an urban setup, that usually means a corner, behind a solid planter, or against a wall rather than in the middle of an open balcony. If you can, group chairs and tables together and lock the casters. Wind loves gaps and light objects, so a tighter arrangement is much less inviting.
Weight is your next best friend. Use weighted bases for umbrellas and parasols, and fill them with water or sand according to the manufacturer. For chairs, sofas, and tables, add sandbags, heavy planters, or purpose-made weight bags to the legs or frame. Don't just put a heavy object on the seat; if the wind gets under the furniture, the whole piece can flip.
Anchors and straps make a big difference. On balconies, use bungee cords, cam straps, or ratchet straps to tie furniture to a sturdy railing or wall anchor, but never to something that could pull loose. For hard surfaces, look at removable anchor plates or ground anchors suitable for your patio. Check with your building if you rent or live in an apartment, because drilling may not be allowed.
Cushions and small items are the first things to go. Take them inside, put them in a storage box, or secure them with clips. Lightweight décor, trays, and folding chairs should be folded and stored when strong winds are forecast. If you have an umbrella, close it and secure it, or take it down entirely; an open umbrella acts like a sail.
A windbreak can help if it is safe and allowed. A sturdy row of planters, an outdoor screen, or a glass balustrade can reduce wind, but don't create a makeshift wall that could blow over. Keep furniture away from the edge, and make sure nothing can fall onto the street or a neighbour's balcony.
Finally, make it a habit. Check the forecast, secure or store loose pieces before the wind picks up, and inspect straps and weights regularly. It takes a few minutes, but it beats chasing a chair down the street.