Two parts to this question - how to ease off an old grip that you may want to reuse (ie cutting it off is too destructive. Followed by how to fit the new one.
I use a thin old electrician's flathead screwdriver to gently lever the edge off the grip up, then tilt the bike so that it leans to the side I'm working on, and then squirt a splash of water and dishwash liquid from a spray bottle into the raised edge. Then withdraw the screwdriver and work the grip around. You can feel it loosen and then it just comes off.
To fit the new one, you simply push it on and position the angle before the soapy water dries.
Once the water evaporates the dishwash is left behind, providing somewhat of a tacky adhesive. So yes this will leave it slidey for an hour or so while the water dries. You can speed this by leaving the bike in the sunlight, black/dark grips should dry quickly.
Personally I'm a big fan of the grips with palm support, but you need them tilted to the right angle before the soap dries. Then tighten the tiny restraining bolts that many new grips have now.