I have noticed that when I put my Blazer in reverse, there is a slight clunking noise just as it engages. It also happens as I put it in drive or when I am coasting and 'goose it' (enough with the animal references) a bit.

In my limited knowledge, I believe it is a UJOINT issue, hopefully not anything else.

Question: How do I check to see if the ujoints need to be replaced?

Thanks.

 

It could be a u-joint.
I would put the rear axle on jack stands, put the transmission in "N", then grab the diveshaft and the differential yolk and twist back and forth to see if there is movement in the u-joint. There should not be.
Use this method for all the u-joints. The only other way is to remove the driveshaft, then remove (carefully) the u-joint cups and inspect the needle bearings and the internal surfaces of the u-joint and cap for wear.