Unlike other MMORPGs you might have played, Fellowship is a Hero-based game, rather than a character or class-based game. This comes with some unique differences, especially when it comes to leveling/gearing alts.
How Alts Work In Fellowship: Gearing
A note before we start: this guide is targeted at players who have already progressed quite far through the game and are now looking at playing other Heroes. If you are still early on in the game, for example in Contender, then setting up new Heroes is pretty straightforward. Just run Quickplay and progress as normal.
Fellowship is a game that encourages you, through its alt-friendly systems, to try out different Heroes. Once you have progressed through Adept and timed Cithrel's Fall on your main, you will be able to buy 75 ilvl gear from the Equipment Vendor for any Hero, and timing Heart of Tuzari will open up 135 ilvl gear.
Note: Method has a full set of detailed Hero Guides from some of the best players in the game to help you quickly pick up new Heroes.

Greens are unlocked after Citrhel's Fall, Blues are unlocked after Heart of Tuzari.
Farming Supplies in Fellowship
So, once you get your main to Adept / Champion, the most important currency you will need for your alts is Supplies. As all 'Currencies' are shared between all of your Heroes, your alt can use any Currency farmed by your main and vice versa.

Supplies can be used in Fellowship for skins, mounts & importantly for us here: catch up gear.
Your main character will have stocked up on Supplies while getting to Adept+, but if you need to farm them then there are three options:
- Keep your Marks of Fellowship and spend them on Supplies; or
 - Spam Quickplay.
 
Quickplay is the fastest way to farm Supplies, and you can use every Mark of Fellowship to buy Supply Boxes. The last Currency to discuss is Gold, but it's quite valuable for progression so you may want to hold off on using that. Once you have enough Supplies to buy gear for your alts, visit the Quartermaster in the Stronghold. You can find him here:

Using Alts To Support Your Main Hero
Your main Hero will need a lot of gold. Once you get to Adept+, investing in upgrades at the Blacksmith is very costly, with upgrades at Champion costing often more than 80 Gold each. To get this gold, you could just spam dungeons with your main and scrap useless gear, but this loop can get a bit boring. If you are working on alts, this is the time to consider using them to support your main.
There are 9 Heroes in Fellowship, which means 9 individual Reward Trees. The base tree has a good amount of Currencies, but you can also try and complete the Contender track. With 75ilvl+ gear, you could also do Citrhel’s Fall pretty easily, giving you even more rewards! Then with 135 ilvl, Heart of Turazi is also a walk in the park.
You can farm a good amount of Gold on every new Hero by playing the first 16 dungeons. To be efficient, you want to finish the Contender track at the same time as you are finishing the base reward track.

The reward tree is a great way to discover and try out new Heroes while still progressing your main.
Once you get a good gold amount, invest it on your main Hero to increase their power level which will help you time harder dungeons in Adept+. Starting a new tier can be pretty hard as the ilvl jump is quite severe. Trying out new Heroes can be a great way to break up the grind while still progressing your main through farming Currencies.