i agree with C.E. to elaborate in case of doubt... if you grab the driveshaft on either side of the joint, try to turn them against eachother. twist back and forth. there should be no slop. if any is felt, replace them asap, as mentioned. imagine the driveshaft whippin around under the car, hitting everything it can find. it will take out brake lines, etc. not cool. there are two. one front and one rear. generally, the rear seems to go out about twice as often as the front. my experience.
the trans mount stuff is right on and better than i could have described. Chevyeater-
the trans mount is only around 10-15 bucks for parts store replacement. piece of cake to do. on mine, i had to transfer a metal bar in it to the new one. poly mounts are around 35 bucks, if you want to go that route. u joints from parts store are under ten bucks. get as heavy duty a unit as you can.
if its a u joint, you can use a drift (read socket and hammer) to drift the caps out. or you can get a loaner ball joint press. its a big c-clamp, and i think it would work (i used a 6.5 inch clamp when doing mine and its a pretzel now). no good if they are stuck. you dont have to R/R the driveshaft to do them, though it is easier for some (i dont cuz im lazy and dont want to remove the exhaust). also, mark the drive shaft and pumpkin flange so it bolts up the same. also mark each end of the driveshaft before you remove the u joint, so you can put if back together in the same orientation. the driveshafts are dynamically balanced. if you get them oriented wrong, you could get some vibs. not good for the driveline. easy job. anyone can do it (in case you have doubts). good luck,
pretty easy stuff.