When mine gets stinky I replace it. The process is fairly simple.
1) Make a template.
a1) Wrap grip with Seran Wrap.
a2) wrap that in masking tape
a3) carefully cut up the seam line and unfold it
b) take off your old grip and use it as a template
2) cut a new set of leather with an extra inch or so on both sides of the seam to leave area to clamp with
3) prep the surface of the grip by cleaning it free of dirt, grime, oil, etc
4) use contact cement on bow in grip area and leather
5) wrap tightly around grip starting on the string side, pulling leather tight to conform to the contours of the bow
6) clamp it together at the seam area with some binder clips, clamps, whatever and wait for it to dry
7) trim off the excess from the folds where the clamps held it into place and taught
8) Stitch it back together to make it look finished.