Here is a basic tutorial that requires simple jewelers and forging skills and tools.
To make a 6mm wide damascus band with a silver inner band you will need a 8mm wide strip of 20 gauge silver, long enough to make a circle the size of the finished ring (about 3"), and a 1/4" thick slice off the end of a 3/4" round billet of twisted damascus.
Take the strip of silver and hard solder it into a band the size desired. Pickle and round out to the desired ring size, leaving the slight taper in the band from the ring mandrel. Set aside.
Take the damascus disc and drill a 1/4" hole in the center. Using a tapered mandrel (drift) , bring the donut shaped disc up to full forging heat and stretch/forge until it is about the desired ring size. Sand/file out the inside, making it larger ,until it will snugly fit on the inner band (from the slightly tapered side). Take off the silver band and set aside again. File the sides straight and bring the damascus ring to about 4.5mm wide. Now start filing the thickness until the ring looks like a wedding band about 2mm thick and 4.5mm wide. Harden,quenching in oil, temper at 500F,then sand and polish. Etch, then blue (and re-temper) it in niter bluing salts .(No worry about tempering too high,500-550 is OK, It isn't a blade. The reason for hardening is to give it as much rust resistance as possible, as well as wear resistance.You can skip the hardening if you want to.) The bluing will often really accentuate the pattern of the damascus, so try it. You will end up buffing it out later.
Slip the band on the flat silver circle. Peen the edges up and onto the sides,capturing the damascus. Go from side to side as you go, so the edge rolls up about 1mm on each side. Slip the ring on the mandrel and work the silver band tight to the damascus band. Clean up any dings in the silver, buff up, re-blue if needed/desired, enjoy your band.
Since resizing is not an easy process with this ring, make it a tad loose fitting and stay away from the Twinkies.
I'll try to put one of these together this weekend and take photos of the process.
Hope this gives you the idea how to do this.
The inner band could be gold, and the damascus could be mokume - you are the artist!
BTW, most damascus makers would be glad to cut off a small portion of the end of a round twist bar and sell it to you for little or nothing.
Stacy