This sounds like the birfield joint is going. It's similar to a cv joint or U joint. Un fortunately with the Samurai you will need to replace the whole axle.
To get it out you need to remove the hubs, brakes, rotor and wheel bearing assembly, the backing plate and then the axle will pull out.
To describe how to do it here would take for ever so I suggest you get yourself a manual from Suzuki and it will guide you through.
It's a messy job anf it takes a little time if your new to it but it is not too difficult. It's also a good opportunity to check your wheel bearings, kingpins, axle seals, and knuckle seals and felts. If any of this stuff is bad you may want to check the other side.
Don't be overwhelmed as if you do need to rebuild all of this your truck will drive much better and your steering will be tighter as well. It will also be good for a few years to come depending on how hard you wheel it.
Good Luck