Pound stakes into the ground around the perimeter of where your flagstones are to be placed.
Attach a string to all of the stakes, forming a string perimeter that will soon be the outline of your newly laid flagstones.
Dig out the area inside the string down 6 inches from the surface.
Place salt-treated 2-by-6 lumber around the edges of the string border. Set them on edge against the inner walls of the dug-out area. Drive stakes in front of the boards to hold them in place. Drive nails through the ends of the touching boards from one to the other, creating a solid barrier.
Pour 4 inches of sand in the 6-inch hole that you dug and wet it down with a garden hose. Compress the sand with a hand tamper by pounding all of the sand down forcefully.
Mix a mortar made of two parts sand and one part cement; add water until you have a stiff but manageable consistency.
Pour mortar into a small section of the patio hole and level it to 1 consistent inch using a trowel.
Set the flagstones where you want them to be and push them firmly into place. Wipe away any excess mortar on top of the flagstones with a wet sponge.
Apply more mortar to another section of the patio and lay a new set of flagstones and wipe away any excess mortar. Continue this process until all of the flagstones are in place.
Mix your grout according to the directions on the container and place it into a grout bag. The grout should be the right consistency to stay on a putty knife without running off, but it should not be in large clumps either. Squeeze the grout into the joints between the flagstones and smooth it into place using a damp sponge. Wipe away any excess grout using the clean end of the damp sponge.
Wait a day for the grout to set. After 24 hours, mix nine parts water with one part muriatic acid to create a cleaning solution. Mix a five-gallon bucket with half a gallon of muriatic acid and four and a half gallons of water. Clean the flagstones with a sponge dipped in the mild acid solution to remove any film left from the grout application.