[Ant]

The best way to grease a CV Joint,
if the boot is in good condition, obtain proper CV Joint grease and appropriate metal clip, remove the rubber boot, and take the old clip off carefully, if you are going to try and re-use it, and repack the CV with clean grease, applying it to the needle roller areas. This sort of operation is very basic and easy to do, if you dont have available a Sykes Pickavant type CV strap clip tool, a set of vice grips and a screwdriver will suffice to get tension on the clip, by taking up the slack and gripping the clip a small distance out with the Vicegrip tool, and levering with a screwdriver, and bending the tail over and under the tabs!!

CV Joints dont have much if any slack in them unless worn, and generally speaking differentials have about 0.006" -0.008" backlash, but the spider gears can have some slack in them, it depends where you are testing it from!!!

You maybe wise to get a mechanic to check it out, or get a workshop manual!!