Remove item from a list after I pick it

I want my code to pick a random number between 0 and 99, and then do it again 99 more times without picking a duplicate. I know how I'd do this in a very inefficient way (pick a random number and then check it against all numbers already picked, repicking if it is a duplicate).

I am sure that there is a better way, I just am not sure what to call the correct structure and thus I'm having a hard time getting the google results I need to figure this out.

What I think I need to do:

1. Build a "list" of 100 items, numbers 0 - 99.

2. Pick 1 item at random from that list, which will remove it from the list.

3. Pick from the entire list again, this time the list is 99 items in size.

4. Repeat until the list is empty

What is this called and what are the key concepts I need to understand?