This is not to my knowledge supported by the rules, but...
I think wrapping the arrow tips in cloth and soaking them in oil should suffice. Light it from a torch just before it is fired. An ally could hold the torch, or it could be stuck into a wall or the ground. A 5 to 6 foot long torch is great for this. You could reduce the effective range of the arrow and/or simply apply a -2 to the attack role. I would apply no more than 1 additional point of damage, unless there is a special circumstance. Alternately I would allow the flaming arrow a chance to light ojects on fire, such as in the case of a house, wagon, or hay.
I believe this is more or less how we played it in 2nd edition. Honestly, I haven't encountered it since 3rd edition.
I would have it so the arrow is on fire, and sets anything it strikes on fire. There are actually rules for this in the Environmental rules section.
Characters exposed to burning oil, bonfires, and non-instantaneous magic fires might find their clothes, hair, or equipment on fire. Spells with an instantaneous duration don't normally set a character on fire, since the heat and flame from these come and go in a flash.
Characters at risk of catching fire are allowed a DC 15 Reflex save to avoid this fate. If a character's clothes or hair catch fire, he takes 1d6 points of damage immediately. In each subsequent round, the burning character must make another Reflex saving throw. Failure means he takes another 1d6 points of damage that round. Success means that the fire has gone out—that is, once he succeeds on his saving throw, he's no longer on fire.
A character on fire may automatically extinguish the flames by jumping into enough water to douse himself. If no body of water is at hand, rolling on the ground or smothering the fire with cloaks or the like permits the character another save with a +4 bonus.
Those whose clothes or equipment catch fire must make DC 15 Reflex saves for each item. Flammable items that fail take the same amount of damage as the character.
Just have your arrows wrapped in some rags or cloth (free) and soaked in Kerosine Oil (costs 5 Gp), light it just before firing it and away you go. No need or any penalties as all you are doing is firing the arrow.
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It depends on what your player wnats to do with those arrows.
Does he want to set something on fire or does he want to deal fire damage to people/monsters?
There is a fire dealing arrow in the rules (slow burn arrow I think) that is very expencive but deals a significant amount of fire damage (1d6 if I remember right).
A normal arrow will not deal much fire damage. As starting point look at the rules for using torches as weapons. Those count as improvised weapons (-4 to hit) and deal 1d4 bludgeoning damage +1 point of fire damage.
So I would rule that a home made fire arrow (Arrow + piece of cloth + flamable oil) would count as improvised, deal damage as an arrow 1 size smaller (1d6 for a medium sized longbow arrow) +1 point fire damage.
If you hit something flammable it has a chance to catch on fire.
I'd just say one extra point of fire damage and leave it at that. Having to set up the ignition source and so forth is enough of a penalty. Maybe they catch the target on fire, especially if its not a wet climate.
Or just get your local wizard to cast flame arrow.
It depends on what your player wnats to do with those arrows.
A normal arrow will not deal much fire damage. As starting point look at the rules for using torches as weapons. Those count as improvised weapons (-4 to hit) and deal 1d4 bludgeoning damage +1 point of fire damage.
So I would rule that a home made fire arrow (Arrow + piece of cloth + flamable oil) would count as improvised, deal damage as an arrow 1 size smaller (1d6 for a medium sized longbow arrow) +1 point fire damage.
If you hit something flammable it has a chance to catch on fire.
I would use these rules and half the arrow's range increment as well
Dotting this to read at home