A concrete patio is a nice, firm surface that allows you to have an outside living area, but it's fairly plain as it is. If this is what came with the home you currently live in, you can spruce it up without having to tear it out and start over. Consider laying paving stones over the concrete to give the patio a more stylish look. You can do this construction worry free, because with a concrete base there won't be any stone separation issues to deal with later.
Sweep the concrete patio.
Mix up a batch of cement and sand to use as a base to attach the stones to the concrete. It should be a mix of one part cement to three parts coarse sand.
Spread the cement mix in a small area that is big enough for a few stones. Start at one corner. Smooth out the cement.
Place a paving stone in the corner and line it up with the edges. Press it in slightly to secure it in the cement. Set another stone next to it, starting a row across one edge of the patio. Use spacers to keep stones apart, about 1/4 inch to 1/2 inch.
Cut the first stone intended for the second row in half, using a wet saw. This way, when you put it in place the seams of the second row will be staggered with the first row. Lay down the paving stones in the second row after you place the first half stone down. Once the second row is in place, repeat the process for the first and second rows over and over until you reach the end of the patio.
Let the stones and cement mix dry and cure for a week.
Mix cement and sand as you did before and fill in between the cracks. Smooth the filled cracks down and wipe away any mixture that gets on the stones. Allow it to dry for another week.