Whats the easiest/cheapest way to add privacy to apt patio?

Those inexpensive stick bamboo shades that can hang on a couple hooks, check big box store garden centers..... https://www.walmart.com/search/?query=bamboo%20shades%20porch%20outside54w&typeahead=bamboo%20shades

or you can put a long narrow planter box plant a couple vines and insert a trellis to form a 4' x 6' plant wall between decks.

A bamboo or stick wall, you can make it, to save money, just make a frame or frames, (depending how wide your patio is) with a piece of timber thought the middle to sturdy up the fame, then add on the the bamboo or sticks, spray paint it, if you like a colour, it will be easy to move it, if you movE out one day. On the other hand have a look around in junk yards and see if you can find some old doors with leadlight or cloured glass or some feature in them, and attach them together for something different, you can go crazy with your imagination on this patio, add some living bamboo in pots that grow tall, or are tall if you can get them at a good price and add them in any of these ideas.

I like both of Sharon’s ideas, and I have another one. Get a roll of dark screen, like in screen doors. You can use fine nails to attach it to existing walls and posts, or attach it to simple frames, and even make the frames movable. Privacy from people and birds. ☺️

An easy idea is to add a trellis and then decorate it with some hanging vines

https://www.hometalk.com/diy/grow/landscaping/how-to-make-an-easy-patio-privacy-screen-step-by-step-tutorial-2087206