How can I fix my concrete patio?

What seems to be happening? No enough info to properly address the problem, but here are some thoughts....

Is the concrete not level and does it seem to be at a slant or has uneven dips in the surface.

You can "skim" the surface level, which will not last long. Or you can set pavers in concrete over the area, making sure you get it level...and perhaps a tiny slant away from the house.

Or is there water running onto the patio from higher ground?

If so, you will need to put in either a French drain or either a shallow indention in the ground to move the water away from the Patio.

Or is there water running onto the patio from having no rain gutters?

If the patio has none of the above problems, this can be fixed with adding a gutter and downspout.

atGreat advice from Jeanette - The ground below us moves constantly, and you may have lost your drainage due to settling. I have a concrete patio with poor drainage, and I just stick a sump pump out when it's critical. You could break up the concrete and add some gravel and drainage, then build a deck as high as you wish over the rest. You could also break the concrete in areas and add plants or gravel, to give the water a way to drain. I can't replace my patio, but am considering having lines cut into it to guide the water where I want it to go. Until then, I have a fleet of rubber ducks that I float in my cement pond... Best to you!

Dig a trench 10” wide and 12” deep around all sides of your patio. Fill the long trench with gravel at the bottom 6” and decorative small rocks in the top half. At each end, open part of the trench to run water into your yard, but not toward the foundation. Bank the soil you dug out so that water would flow off the bank into your yard. This might help the grass grow. And the rock-filled trench will help the rainwater drain away from your patio and into other parts of your yard. I really hope this or another idea helps you have a dry patio and a grassy yard. ☺️