The thrifty housewife in the Depression knew how to get as much life as possible out of a single garment, and then when the fabric could be repaired no more, she would cut it up and turn it into some other useful item. Today, you can borrow a little wisdom from your Depression-era sister, and prolong the life of that frayed, stained or simply worn-out collar on a dress shirt. By removing the collar (without stays) from the shirt, turning it over and reinserting the collar into the neckband and resewing, you can increase the usefulness of your shirts.
Use the seam ripper to carefully cut the stitches along the inside top of the shirt's neckband that are holding the collar inside. Fold the collar up to see what you're doing. Insert the seam ripper beneath a stitch until the stitch thread meets the cutting edge of the inner hook on the seam ripper, push the blade against the stitch, cutting it. Proceed with the rest of the stitches on the neckband.
Remove the collar from the neckband. The neckband will now be open, revealing two layers of fabric. Pick the loose threads from the collar and from the neckband.
Iron the collar on the ironing board, and then turn it over so that the former underside of the shirt collar is now the outside of the collar.
Insert the edge of the collar back into the open neckband and pin the edges to hold the collar in place. Sewing will be a breeze because you will simply follow the indentations of the former machine-sewn stitches/holes on the neckband.
Sew, on the sewing machine, using a straight stitch, on top of the "line" where the previous stitches were on the neckband of the shirt. Sew across the collar/neckband to enclose the collar inside of the neckband. Remove the pins as you sew. Fold the collar over, and then iron the neckband with the newly attached, turned-over collar.
You can employ the same methods for dress shirt cuffs. Likewise, if you have a worn-out shirt, but a nice collar, you can salvage the collar by removing it and saving it to replace a worn collar on a different shirt of the same fabric and colour. If experimentation is acceptable, you can even mix the colours of the collars and shirts.
This method doesn't work well for collars that have stays, as turning over the collar places the pockets for the stays on top where the stays would be visible. In this case, save the shirt for when you have a collar that you can salvage from a worn shirt.