@Jazzbass19: they way I see it, the Roman Numerals IS the Nashville numbering system!
You garden variety 12 bar blues will follow the chord progression laid out by Josh (I - I - I - I - IV - IV - I - I - V - IV - I - I), so let’s stick with that and not (yet) worry about some slight modifications to this scheme. This is THE blues scheme/progression. It follows the same sequence no matter what chord you start with (i.e., no matter what the blues “is in”).
So, if someone calls a blues in C, you know you’ll have four bars in C, two bars in F (the IV for C), two bars in C, one bar in G (the V to C), one bar in F, and two bars in C.
If someone calls a blues in Ab, then it’s 4xAb, 2xDb, 2xAb, 1xEb, 1xDb, 2xAb… and so on.
The pattern you play on each one of those bars can be those that Josh suggested: root-third-fifth-root, or root-third-fifth-third, where “root” corresponds to the current chord in any given bar. Thus, in the first example: you play c-e-g-c or perhaps c-e-g-e (for the four bars of C), then f-a-c-f (for the bars in F), and g-b-d-g (for the bars in G).
(Note: all these examples are for major chords (or dominant chords). If the blues uses minor chords, then remember the flat third!!)