Start with cutting your old grip with the sharp tool. Be careful not to damage the graphite, if the shaft is made of such material.
Remove the old grip tape. Use the solvent if you must.
Take the grip tape and tape it to the shaft. The length should extend the length of the new grip with 1". Press the 1'' inside butt of the shaft. If you forget this then it will be trouble later on
Grip tape the length of the grip + 1"
Depending on if the tape solves with water then you dip the grip tape and grip in water.
Quickly press the grip on to the butt of the shaft. Notice that the guide lines on grip must be square with the club head.