You are correct, "thrift" store is a place to buy old/used stuff.
It's not very common, but "to thrift" means to go to thrift stores looking for things: "What are you doing this weekend?" "A friend and I are going thrifting." "What did you do last weekend?" "A friend and I thrifted the whole day Saturday."
I've never personally heard it used, but it may be more common with younger people.