Where to sell junk
Nearly all you can get from NPCs or shops is that - junk, virtually useless for players. There are two kinds of places where you can sell low-end equipment - general stores and fences.
There are lot of stores in Ankh-Morpork and other cities - just check any map and you'll find one nearby. They buy about everything, except stolen or just really worthless and damaged items. Sometimes general store is full and can't buy any more - just wait a couple of minutes or try another store. Shops give much less for damaged items, so it can be good idea to fix it first.
Fences are people that buy stolen items. They always have specialisation, usually clothes or jewelry. A fence will pay more for items of their specialization. Fences in AM are Jim and Sol. Both are in Thieves Guild (a little east from Mended Drum, check a map). Jim is always in a room just north from entrance and he specializes in clothing. Sol is wandering somewhere around Jim and specializes in jewelry. Use syntax "fence /items/ to /Sol or Jim/" and then "nod /Sol or Jim/" or "say yes to /Sol or Jim/".
You can find complete list of fences on thieves' guild page.
Where to sell useful items
Items that are considered useful by players can often be sold to player shops. What you can sell is mostly depend on your guild skills. Wizards sell spell scrolls; witches sell teas, crystals; priests sell charged faith rods. Different shops specialise on different items, as you can see by looking at shop inventory. Ask shop owners about further details.
Even without any skills you can get some money by scavenging. There are two kinds of it - "search" and "recover". By performing "search" on streets of city you can find some money or item you can sell. Usually you find clothes in horrible condition - fix them by Gapp's low altar or other means before selling - you will get much better price that way.
Other way is "recover". Most high-level players don't bother to loot everything from things they kill. You can "recover" corpses they bury and see if they have something sellable. Just don't forget to bury them again afterward.
Also, in Ankh-Morpork you can check the river Ankh where it encricles the Isle of Gods, where the river is so polluted that it has a crusty surface on which you can walk - though be careful to not stray too far, as the river becomes considerably more liquid further away from the Isle of Gods. Players often kill NPCs on top of the bridges that connect the Isle of Gods to the rest of Ankh-Morpork, and shove their corpses onto the surface of the river underneath the bridge. Additionally, it can be worthwhile to have a look at the surface of the river behind the Mended Drum ("jump down" outside the Drum's back door - but beware, you might trip and land in smelly goo as well as hurt yourself in the process). Corpses of people killed in Drum fights are thrown there and sometimes "authors" of these kills don't bother to go and bury them.
All-time favorite method of getting gold in MUDs - killing stuff for loot. It's fun, it gives XP and TMs, and it's comparably safe if you pick your targets wisely . Use command "consider" to get estimate of how hard would be killing of particular NPC. Check How To Die for info about some specifically dangerous NPCs. "Look" at him/her to get estimate of potential loot. And be ready to flee if things go nasty. Good targets in AM are thieves, merchants, lawyers, bankers and such - though some of these might have bodyguards protecting them. If you aren't going to run to general store after every fight or two (that could be an option, if there is one store nearby), don't loot everything on corpse. Loot just money and things that looks valuable enough for their weight, like jewelry and silk items.
Stealing is a good skill with which to get (or save) some quick bucks. The covert.manipulation.stealing skill is used for both pickpocketing and shoplifting. If you are not a thief, stealing will be a little harder, as you don't have this skill as primary, can't steal in Ankh-Morpork (well, you can technically, but then you will soon wish you couldn't) and you can't predict chances of shoplifting.
Both stealing and shoplifting are nearly risk-free. You will have nearly no serious consequences for shoplifting, and if you fail an attempt to steal from someone, you will be attacked, but you can just run away in that case. As a non-thief you can steal items from someone's inventory and money purse, and snatch items from their hands. With a 200+ bonus you will have a good chance of stealing money from about anyone.
You can try to shoplift about anything from shops - if you are a thief, it will help to learn the case and scope commands to determine how easy it is to steal something. Difficulty of stealing is dependent on item cost and weight (the more, the harder) and shop's base security level (usually higher in bigger cities, except Ankh-Morpork). Each time you (or anyone else) is stealing or trying to steal from shop, the shop's security level is raised slightly. Overall, with moderate skills you can only reliably steal light and inexpensive (~10A$) items. Both jewellery and clothing are usually not heavy and can be sold to appropriate fences, so those are good stealing targets.
Bes Pelagric family missions
In Bes Pelargic, the noble Fang, Hong McSweeney, Sung, and Tang families pay about 10-20 rhinu and 20k xp for mission. Considering that, with some practice, it takes about 3 minutes to do one, it's not that little. The main drawback is that you can only do a mission once in half an hour, so this method is suited mainly for idlers.
Guild specific methods
Only a brief list - consult your guild page for details.
Stealing, obviously. Everyone can steal, but as a thief you a have stealing skills as primaries, thief-only commands and Ankh-Morpork as a playground.
Scribing scrolls. Non-wizards can cast spell from scroll if they have a skills, but scrolls are one-use only, so they are in constant demand.
Brewing teas and other potions, and making crystals. Most player shops that stock tea will buy healing tea with a BWB (brewed with bonus) of 300+, and some player shops will sell 'newbie brew' at lower bonuses to give young witches a revenue stream, and other young characters affordable access to healing tea. Witches can also enchant items up to 'a steady octarine glow' (level 5) for a fee. Although high-level players will want high enchantment from a wizard (up to radiant) on their items, levels of enchantment 1-5 can be useful for low to mid-level players.
Faith rod charging, especially if you have longsight ritual. As a Pishite - donations for resurresting, restoring and pet raising.
Inhumes are the assassin's 'day job'. Covert skills allow assassins to steal legally outside of Ankh-Morpork.
Banditry, killing and looting.