To unlock the third weapon slot, you will simply need to buy the perk. It costs eight perk points. See our perk points guide for tips on how to bag those.
For the fourth, you will need to have a confrontation with one of the Seeds – one of the cult leaders dotted around Montana. The first you will likely encounter once leaving the tutorial island is John Seed. He lords over Holland Valley, his catchphrase, ‘Yes’, erected on a distant hillside like a messed up Hollywood sign.
You need to fill up John Seed’s progress bar to face off with him. Do this by completing missions, side quests, freeing civilians, liberating compounds, blowing up cult property, and killing cult VIPs. Every third of the bar will trigger a story mission.