Legendary items are the gold coloured ones. This will drop from regular play, no need to force it. I got my first legendary around level 15 on world tier 5. Higher world tiers will give you a higher % to get legendary drops but the game can be brutally punishing if you turn the world tier up too high, especially if you play solo like me.
*Edit* From the comments, it seems people are way over level 15 without a single gold drop. I played the campaign Solo, that might have given me a higher % chance of gold drops. I am now level 28 and have 4 gold weapons. Still no armour though, but I am at world tier 6 as anything above that on solo is just punishing and not fun with my current setup. I play a Pyromancer.