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Once you've selected your mat or mats, you'll need to cut a backing the same size as your mats. Backing can be made from matboard or foam-core. Cut a window out of the backing that's a quarter inch larger all around the mat window. Attach double sided stitchery tape all around the edges of the cutout piece; this will eventually be the back side.
Mount the backing - the piece with the window cut out - on the mat with double sided tape.
Center the cross-stitch in the window, then press the cutout into the window (the side that does not have the stitchery should be facing the back of the cross-stitched piece.) It may take a few tries to get the stitchery centered properly in the middle.
Select a corner that looks the closest to how you want the finished piece to look, and start pulling the fabric through the backing and adhere it onto the stitchery tape on the back. Work from that first corner and go all the way around. You'll probably have to make readjustments by pulling on certain parts once more or even several times until it is right. When done, tape the backing into the window with framing tape. Cut a sheet of scrap mat to fit over the back of the piece.
Finally, fit the "package" into your selected picture frame and secure it. Use craft paper to back the frame and then attach your choice of hanger, either a sawtooth hanger or eyehooks with picture wire.
Glass or No Glass
The climate and the location in your house in which this piece is to be hung have a lot to do with making the decision as to whether or not you should use glass, commonly referred to as glazing in the framing world. In very dry climates, it's best to use glass. Accumulation of dust can seriously affect the fabric of an unglazed piece of cross-stitch.
If the piece will be hung in a kitchen or bathroom, where it would be subjected to humid conditions, it's always best to glaze it and make sure it's sealed tightly. The high humidity in these areas can cause severe damage to the fabric. If it's not properly sealed, then condensation will form on the glass and that can cause mildew and mold problems.
If you are living in a humid climate and never get a dry day where relative humidity is less than 20%, it can be difficult if not impossible to create a sealed frame package that won't have moisture problems. Professional framers actually build humidity controlled rooms for this very purpose. So if you live in such a climate, take your cross-stitch piece to a professional framer to seal it or leave it unglazed. If you do leave it unglazed, avoid hanging it in a kitchen where airborne grease and oils could ruin your fabric.
So keep these tips in mind, and you are sure to end up with a beautifully framed cross-stitch that you will always treasure.