how is Gadolinium mined or collected?

Answer 1

Lanthanides are typically found together in mixtures, because their chemical properties are very similar. The minerals are usually crushed and then the really hard part begins, which is the separation because they're all so similar. You can read more about it here, and wikipedia also has entries for the purification methods described if you want to know more about those.

http://en.wikipedia.org/wiki/Gadolinium#Occurrence