You bought a Grand Cherokee second hand, it is missing the owners manual and you are wondering how to shift into 4WD. And when. And why.
You can shift between 2WD, ft 4WD and pt 4WD at any speed back and forth while driving (since the Grand Cherokee does not have manual or automatic hubs you can always "shift on the fly"). There is no advantage in stopping. In order to shift into part time 4WD Low you must be at a standstill - tranny in neutral of course.
Since there are many other 4WD systems than the Jeep Grand Cherokee around - the shifting procdure can be different. I'll add more versions as time allows. Check here for the Mercedes Geländewagen.
Which four wheel drive setting should you chose?
You can use the full time setting at all times on all surfaces. On snow and ice you can use either full time or part time. Part time has better climbing abilities on steep slippery driveways but it has slightly negative effects on the steering. So, to get to your house on the hill, use part time - to drive around town and on the freeway, use the full time setting. If snow gets really deep and you are going slow anyway, use part time 4WD - but be very gentle on the throttle, as the higher torque of low range makes the tires spin more easily.
Part time low is an exclusive off-road setting - don't use it on anything slippery (too much torque - not enough traction). And don't use it on dry pavement either. Same is valid for part time high. Do not use it on dry pavement! The damage will be very expensive.
I accidentally drove my Grand Cherokee in part time 4WD once. It made the transfer case explode. Including towing, a $2,000 goof.
Hubs (in case you stille have them) - to lock or not to lock?
Now, when to lock the diff(s) - to lock or not to lock?