Mod cards can either be bought in packs from the Mods menu during a race or in the main menu far right under the 'options' menu or they can be won from the prize spins.
If you're going to buy Mod packs they cost:
Each pack gives you 5 Mod cards and the more expensive the pack the better the reward. This will take 9 or more packs since the one you're given at the start counts. (Thanks Lavindathar
for the info)
The achievement only counts collecting 50 unique mods since repeats do not count, thanks to Xonatron
for confirming, so try to mix up which packs you buy. You do not need to have 50 Mod cards in your possession at once, just have collected 50 different total in your career, thanks to HSV4ME and ljwaves for confirming.