I suggest that you make a practice piece before attempting hem-stitching on a precious piece of stitching. Cross stitch a box say 3" x 3" - you can always fill in the centre with a motif or two once you are satisfied with the results.
Working on the back of your fabric, count out three threads away from your stitching at approximately the halfway point of the design and, very carefully, lift and snip the 4th thread. Unweave the cut thread back to where it intersects with the cut threads from the sides. Repeat for all four sides.
Thread a tapestry needle with one of the hanging linen threads and weave the cut threads away from the sampler towards the outside edge of your linen. Repeat for all four sides. Your fabric should look like the fabric was woven with a missing thread in a box all the way round your stitching.
You now need to create the hem by removing more threads from the sampler. Starting at the top and counting from the missing thread space, count up 9 threads and completely removing the 10th thread. From this missing thread space count up 8 threads and remove the 9th thread and again, from this missing thread space count up 7 threads and remove the 8th thread. This will be your 'cutting line'. Repeat the above on the remaining 3 sides of your sampler.
Now to mitre the corners. Fold the fabric into the corner and cut the excess fabric from the corner and continue to fold the sides in the same way and pin in place. Baste the hem in place with a basting thread and remove the pins. Do not try to miss out any of the steps as it is far easier to hem-stitch with a basted hem than a pinned hem.
Now for the actual hem-stitching. Start hem-stitchig the folded edge in place, by using an away waste knot which can be removed at a later stage. When you reach a corner, stitch the corners closed on the mitre with an invisible stitch up the seam.
All of these pictures can be enlarged for a closeup view of each step by clicking on them.
Below is Sew Buttons that I used for the step-by-step pictures which chart is still available *here*