How do I refurbish a concrete patio?

You can repair the cracks and then paint over it - either a simple one color or you can paint/stencil designs on it. There are special paints and application tools - ask the pros at your home improvement store for help picking them out!

I would try painting it with cobble stone pattern (use the stone making form turned upside down to paint the design then paint each stone 2 or 3 colors), or draw your own stones and paint them. You could consider painting a "rug" look that would hide the cracks. There is filler for cracks too before you paint. Here is a faux flagstone video: https://www.hometalk.com/diy/outdoor/patios/faux-flagstone-patio-36755668

Faux Flagstone Patio

I had the same issue and this is what I did.

You MUST wet the concrete that's already there before adding to it. If you don't, it will pull the moisture from the new too quickly and make it brittle, making it crumble and your hard work will be for nothing making you say words your kids didn't know you knew. ;)

This is what I used: Skarete 70-lb type N Masonry Cement and Quikrete 70-lb type S Masonry Cement. I used a 50/50 mix. Keep it moist. I used a yard sprayer for mine. I kept wetting the bucket and area where I was spreading. Also you can add bonding agents if you'd like. Since I wasn't going to drill the holes and place rebar to assure the new concrete layer didn't move from the old, I used a gallon of Quikrete Bonding Agent with cement wire. I thought it wasn't good stuff until it set up and hardened. I was pretty amazed. I refaced the sides with large rocks from the yard without bonding agents. The mixture is pretty good.

I mixed mine with a steel spiral paint mixer and drill in a bucket and had a spare 5 gallon bucket of water to rinse with. You want the mixture to have the consistency of stiff moist pudding. You don't want it to dry too quickly because it will become brittle. I drenched the concrete until it would accept no more water. Puddles left are fine as long as they are thin. Get your trowel and spread your cement mixture. Then add your precut concrete wire mesh and top it off with more concrete mixture. If this is a high traffic area I recommend using the bonding agent. I mixed mine in with the water and it was still strong. Very, very strong. I beat mine with a hammer and it held up. I was impressed. Keep your tools clean while working, but if the cement does set up on your tools a hammer will take it off. Or a chisel.

When it starts to set it's easier to spread out and smooth. If you don't want a smooth surface, take a stiff brush and make your marks. Finishing the sides can be fun. You can use decorative stones or the rocks you have around your home. They don't have to be flat. I'm trying to find the wall I started at the old house before I moved. When it starts to set spray it with water and take your trowel and smooth it to a smooth surface. You'll figure it out. You're smart. You got this.

Can you build a wooden deck that just sits on top? We had an old cracked cement patio and we installed a deck over top. Best thing we ever did.