Experience Points can be gained in Trollslayers in four different ways:
Exploring new and unknown lands, or areas unknown in an otherwise civilized area, will grant a character 50 EP x the difficulty level of the area. For a classic 'dungeon', this corresponds to the level of danger, which ofter increases the further down the dungeon one goes. For example, entering a 4th level dungeon and poking around nets you 200 EP. Going from the 1st level to the 4th progressively would gain you 50+100+150+200=500 EP (but you would need to explore something new at each level). For wilderness lands, the difficulty level should be based on the types of monsters and other threats that might be encountered; the outer edge of the Dreadwood might count as 3rd level for this purpose, with the level increasing depending on how far one goes into dark forest, facing greater foes and dangers.
Foes fought (not necessarily defeated, as one can learn from loss as well as gain), as well as other hazards encountered, or other dangers faced (or perhaps even bypassed, if handled well enough), grants EP based on the difficulty of the threat, multiplied by the Average Party Level (APL):
Minor Threat: the PCs are expected to win easily enough, although they may suffer a few injuries, or deplete a few resources along the way - base 25 EP
Serious Threat: the PCs should win, although it is not quite a sure thing, and injuries and lost resources are probably a given - base 50 EP
Major Threat: a fairly even fight, could easily go either way, and the winning side is sure to have serious injuries (if not fatalities) and a serious loss of resources - base 75 EP
Grave Threat: the PCs will almost certainly lose this fight, no doubt suffering serious injuries, fatalities, and much loss - base 100 EP, and they should probably pick their foes more carefully in the future, should any of them survive
Example - Two 4th level characters, a 3rd level character, and a 1st level character (APL=3) encounter three lightly armed goblins. For most of the group, the goblins represent a Minor Threat, and they get 75 EP each for dealing with them. However, the GM might rule that the level of danger is greater for the 1st level character; for him, the fight is a Serious Threat, and assuming he survives he gets 150 EP.
Example - The same party encounter a small swarm of bat-like creatures that also create a hypnotic field, one which is easily resisted by those with magical training. The 1st level character and one of the 4th level characters are spellcasters, the other 4th level character and the 3rd level character are not. For the two spellcasters, the threat is Minor, and they get 75 EP each for the encounter. For the two non-spellcasters, the encounter is more Serious, and they get 150 EP each, assuming they can manage to break free of the hypnotic effect.
A PC gets 10 EP per hour of actual gaming time spent. For example, if a gaming session last six hours (not counting rest breaks, pauses to eat, etc), everyone involved gets 60 EP.
Characters can gain EP based on monetary funds spent in ways that do not directly compensate them (i.e. no EP for spending money on equipment, as that is its own reward). The most common means of doing this are tithing, studying, and carousing:
Tithing - Representing money donated to the church/temple of your choice. This doesn't include any tithings you are obligated to make (for whatever reason). It also doesn't count if you run the temple in question, since you can still access the funds if needed. If a temple of your faith is not nearby, you can also possibly sacrifice the wealth in a manner appropriate to your god, in a manner that means the wealth is no longer usable (i.e. tossing a golden statuette into a lake of lava to appease the fire god). You can gain 1 EP per SP tithed/sacrificed in this manner, with a maximum of (10 x character level x PRE) in EP per week.
Studying - Whether bribing an elder wizard to let you rummage through his various magical tomes, or paying a retired swordsman to show you a few moves, you're exchanging money (and time) for knowledge and skill. Assuming you can find an appropriate teacher, of course. You can gain 1 EP per SP spent on such training/studies, with a maximum of (10 x character level x KNO) in EP per week.
Carousing - What good is money if you don't spend it? Preferably on the fun stuff? This is the advanced art of partying, spending money on booze and whores, and picking up some hard-earned experience along the way via the school of hard knocks. Of course, you need to be in or near some sort of civilization to use this option, preferably a place that doesn't mind getting a little rowdy at times. You can gain 1 EP per SP spent on such debaucheries, with a maximum of (10 x character level x END) in EP per week.
A character can choose either Studying or Carousing in a given week, but not both. They can make Tithings separately during that same week.
Also, because TS is designed to support an 'endgame' of characters building their own keeps, temples, etc., they can also gain 1 EP per GP spent on building/renovating/maintaining such buildings (2 EP per GP if said building is in otherwise uncivilized lands, away from safe, civilized areas.