If the joints are sloppy loose (play) or they are binding in rotation then you replace them. Ask some old parts shop for the "driveshaft cross" - they are same parts in starlet and corolla of 70s and 80s.
by reading most of this forum nowadays it seems that proper shops are dead or dont know mechanical repairs.
The steps in replacing U joints are pretty simple, but you need to wash the shipping grease out of the joint cups and stick the rollers back in carefully with new grease (if your new joint is non-greasable type). If your joint is zerk type then it needs to be pumped till you see fresh grease flow out of cup edges.
The white/clear stuff you see in new brand new U joints is just shipping grease and should not be subjected to normal working load.