Does the vehicle have to be in neutral when you put it in 4 wheel drive, or what is the proper way to engage the 4 wheel drive

Remove the actuator motor assembly from the transfer case and try to manually engage the transfer case, if it is easy to engage then the actuator is the problem.

The best way is to take your time...,Set Emerg brake,start vehicle and put into neutral..Engage 4 wheel drive,look at your dash gauge area for 4 wheel drive light to come on..Put truck in reverse and release park brake..,Back up 10ft.slowly..Then put it in drive and pull up 10 ft.slowly then you should be in four wheel drive..

Your best bet for shifting Dodges are in neutral.

4 wheel neutral vehicle will not move that for towing or moving around --put in 2wh --4hi or if have 4low transfer case has to be in a setting to move

You can shift between 2Hi and 4Hi when the truck is moving. Just let off the gas and shift it. But in order to shift to Neutral or 4Lo you need to stop the truck and shift the transmission into neutral then shift the transfer case.

put your truck in neutral put it in 4 wheel drive put your truck in reverse for 4 or 5 feet then put it in drive and thats it.

SOUNDS LIKE AXLE WINDING UP. ARE YOUR TYRES ALL THE SAME SIZE AND ARE YOUR HUBS FREEING PROPERLY?

Most of those have Quadratrack which is full time four wheel drive. (lever all the way to front) neutral is used when towing your vehicle and low range is only used when in severe conditions or pulling another vehicle from a mud hole etc. That can be engaged by rolling slowly forward and pulling the lever all the way back. On all other systems though some can be engaged at a standstill, it usually id better to shift while rolling, usually below 20mph. Neutral in all systems is as I said before.
If it cannot be shifted, or it does not engage, likely it is either not properly adjusted or the transfer case or another component is worn.

You should be able to put in 4x4 while in drive less than 35mph. Mine had a switch to turn to engage or dis-engage.

As far as I know the procedure should go something like this...

Stop the vehicle, engage the parking brake and if applicable, get out and turn the hubs on the front wheels from Free, to Lock.(You may not have these on a Suzuki, they may be auto-lockers)

Get back in the vehicle and put the transmission shift selector into Neutral.

If you have a manual transfer case, move the selector-shaft to 4x4-High, or 4x4-Low -- whichever is desired. Now, putting the vehicle in gear with the transfer case is sometimes somewhat difficult. As long as the vehicle's transmission is in neutral, don't worry, the gears inside the transfer case are big and beefy -- Don't be afraid to be rough -- Again as long as the transmission is in neutral. You may also have to disengage the parking brake and slightly let the vehicle roll forward or back with your foot-brake to get the Transfer case to lock into place.

Once 4x4 of the selected High, Or Low range is selected, usually indicated by the vehicle jerking slightly with a slightly loud clank/thud. Move the Transmission selector out of neutral into your desired gear (Drive if Automatic, if Manual, whichever gear you pull out from). and voila! You should now be in 4-Wheel-Drive.

To disengage 4-Wheel-Drive. Just reverse the steps.