Fighters Guild Quests
Fighters Guild ("Fighter Trainers" in most desert areas) quests are usually straightforward affairs. In the original version of the game, you should have been able to pick up a couple of artifact quests from them, but the quests were moved to the Knights Guilds with one of the very early patches. Fighters Guild quests can and do improve your rep with the commoners, so if the people aren't talking to you, try completing a few of these to fix the problem. Most of these quests should net you a new dungeon on your map, but it doesn't always work.
"I got a request to dispose of a giant scorpion..." (any rep): the quest must be completed within the game day, so don't take it unless you can find the house before midnight. Disposing of the critter shouldn't be too much of a problem, but remember that Scorpions cast "Paralyze" each time they hit.
"Seems some poor soul brought home a giant spider's egg that hatched..." (any rep): same as with the giant scorpion. It must be completed before midnight and be prepared for paralyzation.
"...chase off some barbarians..." (any rep): a local house and you have 24 hours to complete it. The Barbarian will be the same level as you, but they have more hit points than any of the other canned classes.
"...too menial for fighters of the guild to accept..." (any rep): a local house is infested with giant rats. There will be about 6 or 7 of them. Don't burn time loitering. Just wait and they will appear for you.
"Seems there's a loup -- whatcha call your basic werewolf..." (any rep): there are two versions of this quest. Both involve a standard dungeon crawl, but your object could be either a lycanthrope or merely a bear. While infected with vampirism, this quest only turned up a bear for me, but this may just be my system.
"We have a request from a local citizen. Seems a wild animal has gotten into his place..." (any rep): the house is in town and it's either a bear, tiger, spider or harpy. A real quick quest that can be completed in a couple of minutes.
"Some fool left his back door open and a wild animal got in..." (any rep): this one requires travelling to another town. The critter is either a bear or a tiger and you should also get a new dungeon marked on your map.
"I have a relatively menial job..." (any rep): clear the bats/rats out of a local house. This one is a little buggy. You are supposed to get a message when you have killed all of the, but it doesn't pop up on my system. Also, when talking to the guild to close the quest, I get the right dialogue, but no money.
"...a job just came in for some giant-killing..." (any rep): you not only get to fight the giant you were sent to kill, but also a few of his buddies (about 6 or 7 of them) that start appearing when you hit the original target. Teleporting out of the dungeon doesn't do any good except to limit the number of buddies to four or five who appear with you (careful with civilian casualties -- "collateral damage" for the politically correct) and all at the same time. Occasionally you can rescue a merchant who asks to be taken to a store in another town.
"We have a rather interesting job requiring a bit of brains rather than brawn..." (any rep): you need to retrieve a noble's pet tiger from a dungeon. You will be given a bell. When you find the tiger, "use" the bell and then hit the tiger. The tiger will not respond until you have inflicted some damage on it. Be careful that you don't kill it. I find that unequipping a weapon and using my fist on it (or using an Iron Tanto) is the best way to inflict minimal damage. Somewhere in the vicinity of the tiger you should find a dead body with a letter. The body is "too heavy to lift", but turning to the side will usually bring the letter to the top. Report to the noble to collect your gold and find the person mentioned in the letter to collect a magic item. CAUTION: This quest does not always terminate correctly and fixsave does not fix it. The quest remains active in your logbook until the expiration of the time limit and the letter does not always appear with the dead body. Because of this problem, you will not be able to get another quest from the fighters guildhall that gave you the quest until the time limit expires (I think you take a 2-point rep hit for blowing the quest, but you get to keep the gold and magic item and can sell the bell before the time runs out).
"I have an important mission that will require the utmost discretion..." (rep 11 or more): this is the infamous Lord K'avar quest.
"Seems there's this flock of flying carnivores -- harpies..." (rep between 10 and 20): there are five of them. Fortunately there is a fairly easy way to deal with it. Since they appear randomly, a good trick is to clear the area around the entrance and then loiter or rest for a couple of hours. This will usually cause them to start appearing somewhere in your vicinity where you can dispatch them and then wait for the next one. This doesn't always work, so save the game as soon as you enter the dungeon (good advice regardless of the quest).
"There's this pack of giants that want killing..." (rep 20 or more): six giants. The first one is usually in one of the usual quest object locations and the rest appear randomly. Sometimes resting or loitering will cause them to generate, so you can try the same strategy as with the harpies.
"Standard protection job." (rep 21 or more): not so standard. Don't take this quest in your usual hang-out because the questgiver won't talk to you for about a month. The client is already dead when you get there and you usually get to fight a few assassins. There is a note with the body directing you to the guy who ordered the assassination. You must go take him out (and his buddies) in order to activate the last part of the quest. This will damage your rep with the Dark Brotherhood. Now you have to wait for a month or so (an in the interim, the questgiver won't talk to you because the quest is still active). At the end of that time you will receive a letter from the daughter of the client asking you to meet her in another town. It's a trap and you get to fight a few more assassins. Deliver her to her destination and you will be rewarded with a magic item.
"There's this bad critter in <dungeon>, a Daedroth..." (rep 30 or more): standard dungeon crawl, but remember that you need Mithril weapons or better to hit a Daedroth.
"...it's offing a lich in <dungeon> and it only pays ## gold..." (rep 30 or more): standard dungeon crawl, but remember that you need Mithril weapons or better to hit a lich.
"Bit of a rummy domestic squabble..." (rep 30 or more): the husband is a zombie that comes out at night, so you'll need to loiter until he appears, usually about midnight.
"Some woodsmen have hired the guild to kill a Spriggan..." (rep 40 or more): there are two ways to complete this: kill the Spriggan and report back for your reward or try to make peace between the Spriggan and woodsmen. The Spriggan will offer to deal as soon as you inflict damage on it. At higher skill levels and special material weapons, you will probably kill the Spriggan before you have a chance to work a deal.
"A certain merchant needs to have a monster, a gargoyle to be precise, dispatched..." (rep 50 or more): standard dungeon crawl.
"We have a new client who wants someone to hunt down an atronach..." (rep 60 or more): standard dungeon crawl.