Honestly, the best way depends on how much furniture you have and how much of a DIY mood you're in. For a few lightweight pieces—folding chairs, a small side table, planters—I'd skip the big move-day panic and use a hand truck, a cargo bike, or a friend's hatchback, ideally outside rush hour. Wrap anything that can scratch, strap it down, and take the elevator if you can reserve it.
If you have bulky or heavy pieces—a patio table, lounge chairs, a grill, or anything with glass—the cleanest option is usually to hire local movers who already know how to deal with walk-ups, narrow hallways, and tight parking. If you'd rather save money, rent a van for a couple of hours and ask a friend to help. In cities, book a loading zone or check parking rules first, because a ticket can wipe out your savings.
Before moving anything, measure your doorways, stairwell, elevator, and new balcony or patio. Disassemble what you can, remove cushions and glass tops, bag the screws and bolts, and wrap frames with moving blankets or old sheets. Keep cushions in a separate bag so they don't get greasy or wet. Load heavy items low and against the van wall, use straps, and pad anything glass or painted. If rain is likely, cover everything with a tarp—outdoor furniture can handle weather, but moving straps and cardboard can't.
On the day, move the awkward stuff first, keep a small toolkit handy, and don't over-tie small parts. Once you're in, reassemble before you lose the hardware, wipe everything down, and let cushions dry fully before putting them back out. If the furniture is old, rusty, or too big for the new place, sell or donate it before the move; that's often cheaper than paying to move something you won't use.