The iFixit guide at:
https://www.ifixit.com/Guide/Mac+mini+Late+2012+Hard+Drive+Replacement/11716
has a list of the tools needed. A spudger similar to the one they use in the iFixit guide and one that I have found useful is something similar to:
https://www.amazon.com/Apple-Nylon-Probe-Spudger-Black/dp/B003TOFFNQ
Take a look at this page:
https://eshop.macsales.com/item/OWC/DIYIMM11D2
There's a note in the second column about drive placement and how to find out where your drive without opening the computer. The drive is either in the "upper" bay or the "lower" bay. The position is relative to when the Mini is flat sitting on the black plastic plate. I believe you can swap the drive in the lower bay without having to remove the logic board (removing the logic board makes the operation quite a bit more difficult). I haven't done it this way myself but it appears doable and I haven't seen anybody who says that it can't be done this way. It's most common to have the drive in the lower bay in which case you can do the swap with the easier method. If you have the drive in the upper bay, to swap it you have to remove the logic board, thus you may want to consider buying the OWC kit in the link above and just keep the HDD where it is. You have to order the kit for the upper bay (they sell their kit based on the bay where your existing HDD is). The kit OWC sells also has the screwdrivers (but the spudger they include is not as useful as the one I mentioned above, IMO). The video in the OWC link is one where the logic board is removed. I'll don't have a list of videos using the easier method - I'll take a look and post if I find a useful one.
Another alternative altogether is to just put the SSD in an external enclosure and boot from it. I prefer to put the SSD in the computer myself, but if you're interested in the advantages/disadvantages of doing that, ask.