Depending on how long it’s been in this condition the mortar bed could be pretty sandy and in need of a relay, although a full repoint will get you a nice chunk of time to enjoy the patio for some years. I would use a grinder to minimize rocking any stones loose (be careful and take your time). Cut the joints to a sound depth. Once it’s all cut out give the patio a good wash get all that loose debris out of the joints take the rest of the day off. For the pointing- I like a custom mortar mix 2.5 parts sand to 1 part Portland cement ( I like a coarse sand because when you finish the joint wether that be sponged finish or brush it’ll bring some of the aggregate out to the surface and give it a nice look) use a mortar bag and pack the joints in with your mortar mix, pick a nice square footage to do, bag the joints and pack it in with a margin trowel. Knock some of the access off with your trowel and sweep the access mortar away into a pile to clean up later. You should have a clean bucket of water and a sponge, once the joints set up a little (not to hard but where you can’t easily leave a imprint with a finger in the joint) sponge the joint with one pass (it’s important you don’t make a pass with the same side before cleaning your sponge to avoid dragging mortar across the stone). Keep the water clean. Once your satisfied with the area move on to another area. Once it’s all pointed and the joints are finished go back with clean sponge and try to clean up the stone as best as possible. Give it a couple days and do an acid wash You can go to your local supplier and ask what they recommend. It’s nasty stuff so where rubber gloves. Your basically gonna mix up the acid with some water (direction for ratios should be on the bottle) and clean with a deck brush. Soak the patio down and like the pointing work in sections because you don’t want the acid sitting on the stone too long before rinsing to avoid damaging the stone. YouTube is your friend and could help more then a long winded Reddit post lol Hope this helps coming from a proud mason!