Bill Moran taught me how to do it.
The wood needs to be fine grain,not too hard, and not brittle.Ebony is not an easy one to start on.Curly maple is a good starter wood.The wire is called jewelers wire,and is a flat strip about 24 gage and 2mm wide (get half-hard temper).You make a tool (or a set of them) from old hack saw blades.They look like small engraving tools.The blade is ground to the thickness of the wire,and about 3mm long ( to make a cut 3mm deep).Harden and temper the blade,and mount it in a wooden handle,and sharpen the edge.Make them in 2,4,and 6mm blade widths. 6mm is about as wide as works well. Sketch the design on paper,then re-draw it on the wood in pencil.Start making the cuts by pushing the tool into the wood,rocking it out,re-inserting it just down the line....and so forth until you have cut all that line.To insert the wire,draw it through a piece of folded 120 grit sandpaper to stiffen it and put a slight roughness to the sides.Using a very small mallet,tap the end into the cut and tap your way GENTLY along as it goes in.There is a lot more to it than this,but this should give you the idea.Bill Moran has a video on handles and wire inlay that shows the whole process well.
Stacy