If the player doesn't skip directly to The Tops (such as by sneaking across the Deathclaw highway, waiting for a NCR soldier to die to a Fiend and using their uniform to board via monorail), they've met NCR and Legion if they've followed the crit path. Goodsprings will direct you to go to Primm, and from there you you're directed to Nipton where they meet the Legion (and likely visit the NCR border post along the way). After Nipton you continue to Novac, where you get some more NCR background from Andy, Boon and Boon's partner in Novac and likely run into all the Legion v NCR stuff in that area (Searchlight, the legion camp, forlorn hope ect.). They'll generally encounter plenty of the conflict by the time they're approached to take a side.
Once you hit Benny's, you're actually given plenty of ways to go. Mr. House just outright hires you. Depending on how you dealt with Benny, you may encounter Yes Man who will appeal to power (you could become ruler) and compasion (you've likely seen how the balance of power can screw over the common man). NCR and Legion both call you to meet with a representative who will detail the factions and why they should win.