If the straps aren't broken or loose, I would have to assume the needle bearings in the cup are ground up and rusted away. Replace the u-joint. If you've never done one before, leave it to a professional. If you want to tackle it, remove the two c-clips on the inside or outside of the cups that hold them in place, then use a vise or c-clamp with a pair of sockets to press the cups out of the drive shaft. One cup has to enter the socket with a large enough opening to accept it. If the cup catches on the socket, the ears on the drive shaft can be bent. This will cause a vibration from being out-of-balance.
Pressing the new cups in can be a little tricky. You must be careful that the needle bearings don't fall out or drop down in the cup. One dropped needle bearing will prevent both cups from being pressed in all the way. You won't be able to get both c-clips installed in their grooves. If you try to force the issue, the back of a cup will blow out; then you get to buy another u-joint.
The two other cups slide into the axle yoke and are held in by those straps. The joint must be greased when you're done. The grease already in the cups when you buy it is just there to hold the bearings in place. You will get a grease fitting to install either in one cup or in the middle of the cross. There should be directions telling you which way to position the cross. There's no front or back, and all the cups are the same, but if you put the cross in backwards, you will have a hard time getting the grease gun in there.