There are currently five tiers of legendary effects defined within the game, three of them currently available. Regular items, the RNG drops, can be maximally 3*, some of them containing additional item-specific legendary effect that doesn't influence their 'rank'.
The currently available legendary modifiers are referenced as following groups: prefix effect, major effect, minor effect.
A piece of armor or weapon cannot have two legendary effects from same group, so the Bloodied Instigating or Explosive Fire Rate weapons don't exist. Some of the 4* and 5* effects currently not enabled in regular RNG rolls are already implemented on some named items - challenge and quest rewards. An example would be Bunker Buster with flat +20% damage bonus, or Perfect Storms incendiary Damage-Over-Time effect. These items, despite using 4* or 5* effects, are only 1* legendaries.
The best way to grind legendaries is to visit various places in big group of players. The RNG is getting generous when it sees 8+ players.
If you roll something that you deem useless and unsellable, you can exchange it for Scrip - a currency obtainable only in-game, that you can use to gamble for legendaries. You get to sell up to 150 scrip per character per day, and if you want to sell whole 150, you need to plan your sales accordingly, as you can't scrip an item worth 3 to pick 2 out of the machine. Scripped items give out as follows 3*/2*/1* - Weapons: 40/15/5, Armor: 24/9/3
The RNG itself seems to be a wave, moving at its own pace across all the online servers. Generally speaking, the rolls that are being spread around globally at any given moment tend to be 'themed'. It's very often that even in the periods in which no dupe tricks are being commonly used, different players get same things in rather short intervals.
As a player using two computers and two accounts to test how various things work, quite often I had situation in which for example my main looted Zealots weapon and Ghoul Slayers armor and my alt looted Ghoul Slayer weapon and Zealots Armor.
As a player rolling around with gang, whenever one of us scouts the Purveyor (buys three items to taste the 'theme') and gets promising results, we converge at that players server and burn out all of our scrip from all characters. In such cases, when looking at dozens of 3* items rolled within minutes, the theme is clearly seen.
People ask 'why does the Purveyor only dropped me heavy weapons, I just burned 1000 scrip and only got one non-heavy' - well, this is because they rolled it all during a heavy weapons theme of the RNG wave.