Read at your own risk!
There are various ways to automate or semi-automate the gathering of resources, and even more ways to efficiently and quickly find specific gear. Farming is the process of gathering the resources through the use of repetition and exploiting game mechanics.
Skipping past mobs to get the completion reward, or reliably opening chests is often the fastest way to farm for gear. Using a Ghost Cloak in combination with Boots of Swiftness and other speed boosts/cooldown reductions, it's possible to speed through mobs and get the loot without fighting.
Soggy Cave has various skips with rolling and jumping over terrain. It used to be faster where it could be done in less than 30 seconds using an exploit to skip the puzzles. Mouse-clicking on the door to the chest room while pressing the gamepad's "activate" button ignores the wall normally opened by the puzzles. The exploit was patched by making the mouse cursor disappear when moving with the controller. With cross-platform out, this makes the game more fair for everyone playing together.
Desert Temple has a secret obsidian chest near 2 gold chests and a Piggy Bank. Run to the Key Golem, past the locked door there is a sub-section containing the chests, but there is a bug where the obsidian chest room often cannot be entered, because of the incorrect camera angle. A bit further into the level after the sub-section there is a Piggy Bank and a mini-boss (usually an Enderman).
Various Locations have an unlimited supply of enemies spawning and attacking you. Pumpkin Pastures has a section near the end where two switches must be flipped to lower the drawbridge and continue. There are also various places where Spawners appear.
Auto-clickers and macro programs such as Auto Hot Key make it easy to run a script to fight and use abilities while away.
Health Synergy armor and Final Shout can create an infinite loop, which heals you and activates your artifacts whenever you take enough damage. Of coarse this loadout still needs ways of killing mobs, so a summon or two can be great.