So you're prolly already past this, but for others like me googling this answer:
1. Read the entire description section on the nexus mods page; installation directions are often either listed or pointed to.
2. Download and install the desired mod, per any given instructions. Most often you'll be able to click the Vortex button, but not always.
3. In Vortex, go to Settings>workarounds>BSA Redirection and click the slider so it's highlighted in color. This *should* automatically install and deploy the Vortex Archive Invalidation mod. You probably made it this far already, BUT:
My Vortex wasn't updating my .ini files to show the invalidated .bsa files; I had to manually edi Documents\My Games\FalloutNV\Fallout.ini *and* [drive game is on]\SteamLibrary\steamapps\common\Fallout New Vegas\Fallout_default.ini. In both cases, I opened the the files in Notepad, scrolled down to the section entitled "[Archive]" and edited the first line to read:
SInvalidationFile=
and the last line to add:
Vortex - BSA Redirection.bsa,
to the list of filenames after "SArchiveList=". Remember we're dealing with filenames, so one typo can make it not work. Do *not* add "Fallout -" in front of it.
Remember that version and other mods can change a *lot* of things, but I hope this either helps or gives a starting point for a fix.