The following suggestions are very conservative and cautious. It is safest to list many things of which a stitcher might want to be aware. You are then free to use or ignore whatever you choose.
Trim off any selvage edges, as the tightly woven edge may cause uneven tension in the fabric.
Some people recommend stitching on a project so that the warp threads go from top to bottom, with what was the selvage edge at the side.
Make sure the fabric is actually the count you think it is. Mark one inch of fabric using pins or some other method. Count the number of squares or threads. If the count is very different than what you believed, you will need to cut the fabric to match the true count. For example, if your 32 count linen is actually 30 count, the stitches and the project will be larger than expected. A bigger piece of fabric will be needed.
Cut the fabric to size for the project. Allow at least an extra 3" to 4" on each edge.
Pre-rinse very dark or very red fabrics to make sure the color will not run. Rinse until the water is clear. Obviously, you should not do this if you know the fabric was dyed with a non-colorfast dye.
If there are folds, make sure they will come out. Dampen and press the fabric.
Prepare the edges. Some of the options:
Use a sewing machine to do a zigzag stitch.
Use a serger to serge the edges.
Fold the edge of the cloth over and baste it by hand.
Overcast the edges by hand with a whipstitch.
Use Fraycheck or masking tape, but then allow another half inch (1/2") all the way around so you can cut off the chemically tainted fabric when you are through stitching. Chemicals of any sort may cause deterioration years later.
Let them fray! Many fabrics will only fray a small amount. If the fraying doesn't bother you, just let it happen.