Well, to determine the final grade of your pavers on sand you will need to establish a level to grade the sand to. A string line or 8 foot level can work or you can rent a transit depending on how accurate you want to be. You determine the grade of the BASE of your pavers including drainage and you pound 2x2 stakes or similar supports into the ground at that level. The stakes can be 4 feet apart and need to cover the entire area in a grid. On top of the stakes you lay steel pipes or other rigid material in appropriate lengths. For your job 8 feet is fine. You only do one section at a time so 2 pipes are enough. You put these pipes down on top of the stakes so they are parallel. Now you have 2 parallel pipes roughly 6 feet apart laying on stakes. You put sand in around them till they are barely showing. Place a good straight 2x4 across the top edge of your 2 pipes and pull the sand down the pipes into a level grade. Use a sawing motion as you slide the 2x4 along your pipes. This ussualy takes one person on each end of the 2x4. This is Screeting. Once you have a perfectly level pad of sand around the pipes you pull them up and move them to the next set of stakes. Often you will only move one pipe to the next location and leap frog around the area in this fashion. The depression left after you move the pipe is filled in with more sand and carefully screeted with a short board. Now you can lay your pavers on the perfectly graded sand. Once you have paved in an area you fill and screet the next closest area. In this fashion you gain a perfect grade over the intire area which is established by the height at which you place the stakes. For winding paths a person can use PVC pipe to sit on the stakes and bend to follow the curves. Sometimes it in necessary to put nails or screws in the stakes to hold the pipes in place. Obviously the stakes get barried in the long run. Of course paver edging is used around the perimeter to keep the pavers in place. Once the pavers are placed you put sand over them and use a vibrating plate compactor to seat and level them. Sweep it off, and wash it and your done.

A lot depends on how it was originally laid, where it is, etc. I have some questions for you: Where do you live? (city/state) How thick is the flagstone? How wide are the joints? Are these squares or irregular shapes? What sort of dirt, gravel or whatever is under the flagstone, and how thick is it? (pry one up and dig down to see what's under it) What is different about the damaged side? Was it on an unstabilized slope? Got lots of water?

If it is settling in spots and stones are coming loose, I would NOT try to set them in mortar. They are settling and coming loose because it was not built properly. Setting it in mortar will only compound your problems as it continues to settle the mortar will crack. You do not give sizes, but if the stones are too small, they are not appropriate for a patio and will always come loose, only larger, heavier stones should be used for a patio. You could remove a few stones and check what is underneath. How deep is the foundation, what size is the gravel, etc. Do you have drainage issues, is it sloped properly away from the house. There is no quick and easy fix for an improperly laid patio.

Amjess we have a deep forest green color which i think would look good on your patio.