Most Toyotas are like lego blocks...they snap together. The pro's learn where the right place is to unsnap stuff and you want to use a plastic prying tool to avoid ugly scratches.
When I have to remove stuff I haven't before, I like to look at diagrams which, hopefully, show where the clips or notches are for removal. (Also search on youtube.) For a 2012 Tacoma, I found a diagram here.... Air Vent - Toyota (55650-02250-C1) | Toyota Parts Using your trucks' VIN will ensure you see the right parts.
Ohhh, this stinks big time. You have to take a bunch of stuff apart first it appears. 10 pages worth, with the 10th page being references to almost 20 more steps.
Looking at the factory manual, there are 56 steps to Install the instrument panel completely, ending with the carpet in the console box, prior the console box, cup holder, front console box,......... #5 of 56 is the #1 instrument panel register assembly (whichever one that is). #17 is the trim around it.
I am not even going to go further, you are essentially dismantling almost everything in front of the seats, including footrests it appears. Don't quote me on this, but maybe ask your dealer. Whatever is wrong with your vent, it would have to stop the truck from running before I would go down this path.