How does one craft weapons and armor in D&D? Assume I have a high enough crafting skill to create the item: how do I know what materials I need? What is required to make say, standard scalemail armor?
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Mundane Item Crafting, Step-by-Step
These rules use exclusively the Player's Handbook and Dungeon Master's Guide. I'll gladly upvote answers that take on official sources beyond these.
Let's Craft Scale Mail!
Axebeard MacDwarf is Int 10 with 7 ranks in the Craft (armorsmithing) skill. He has masterwork artisan's tools. He has a +2 racial bonus to Craft skills related to metal, and there's metal in scale mail. His total skill bonus for the Craft (armorsmithing) skill when making scale mail is +11. MacDwarf buys scale mail raw materials, costing an inconvenient sum that the DM permits him to acquire for only 16 gp. The DC for making scale mail is 14. MacDwarf has a week, so he takes it, converting the 50 gp price of scale mail to 500 sp. He takes 10 on the Craft (armorsmithing) skill check for a result of 21. He's made 21 x 14 = 294 sp of progress on his scale mail. Give him another week, and he's done. If he wanted to--or if he was interrupted--, he could track progress by the day, and by taking 10 make 294 cp of progress per day; it will take MacDwarf more than a week if he takes indivdual days to complete the scale mail at that pace, however.
Let's Craft A Picture of That Lady!
The Crimson Lothario wants to impress a lady. He is Int 18 with 10 ranks in Craft (painting) and has Craft (painting) artisan's tools, for a total bonus of +14. Crim set his own price on the painting of 100 gp, and the DM lets him spend only 33 gp on raw materials. Crim's player asks the DM what the DC for nice painting is. The DM consults the table on PH 71 and picks 15. Because he doesn't have a model to work from, the DM rules Crim can't take 10. Crim wants to work by the day (he's got adventures to go on, after all) so the painting's value in cp is 10,000. The first day he spends painting Crim rolls a 15 for a result of 29, making 15 x 29 = 435 cp of progress on the painting. After he returns from an adventure, he has a week off, so he paints and rolls a 3 for a result of 17, making 15 x 17 = 255 sp progress on the painting. Hey, a few more weeks (like, three) and he'll be done.
"Wait a minute. That means...?!"
If you've gotten this far, you might have noticed some--let's be fair--strangeness in these rules. You've noticed that the higher the DC of the item (i.e. the harder it is to make), the faster it can be made. So setting DCs arbitrarily high isn't always bad thing if by taking 10 the craftsman can skill beat the DC. Yes, that means most DMs will rule it's faster for a craftsman to make thieves' tools than it is 10 ft. lengths of chain because most DMs will set the DC for the thieves' tools higher (probably a high quality item) than the DC for the chain (probably a typical item).
That's kind of okay. The number of folks who can consistently make lengths of chain far outnumber the folks who can consistently make thieves' tools, so it's not like there's a thieves' tool glut and chain shortage or anything. But it is still weird.
Welcome to D&D 3.5 economics.
"O, that's too much work!"
You're right. That's why there are shops. But, besides that, you can make it less work. Untrained hirelings cost 1 sp per day, and the Craft skill can be used untrained (PH 64). Your hirelings will need artisan's tools (probably) but using the rules for aid another (PH 65-6) should allow you to simply buy success. The DM may limit the number of assistants you can have (perhaps to just 1 if the DM's stingy about the bonuses from favorable circumstances (PH 64)), but it's an option, especially if you're that close to being able to beat the DC by 10.
The best way to speed this process is via the spells fabricate [trans] (PH 229), minor creation [trans] (PH 253-4), major creation [trans] (PH 252), and true creation [trans] (SpC 224). The DM, however, may mandate Craft skill checks for complex items.
"But where does firewood come from?"
You chop wood with an improvised tool and use the Craft (carpentry) skill check untrained. Firewood costs 1 cp; fractions round down; one-third of a cp is 0 cp; raw materials are free. The DM rules that crafting firewood is DC 5. Spend the day karate chopping trees, taking 10 on the Craft (carpentry) skill check for a result of 8 x 5 = 40 cp of progress made per day (essentially, you're making 1 check every 12 min.). Make 40 cp (800 lbs.) of firewood in a day. Sell that firewood for half price (D&D economics, everybody!) and earn 2 sp. Buy a poor meal (1 sp) and 2 mugs of ale (8 cp total) and put the remaining 2 cp away for a rainy day. Congratulations, peasant. You're alive. I hope your family home isn't threatened by an owlbear so you can continue to take 10.
I take it you've already worked out how the mechanical process of calculating progress for your crafting tasks work - at least, some passage in your question tells me you have. If not, tell me and I will update my answer.
To create, say, standard scalemail armor you need some "materials for crafting armors". These are non-descript (the game does not usually care about this level of detail) and their cost is defined by the cost of your final product.
In the vast majority of crafting, you need to buy these materials from someone, with a few exceptions being maybe dragon scales that you can actually take from a slain dragon.
The Craft (metallurgy) and Craft (metalworking) skills can be used to provide raw materials for any metallic armor or weapon (metallurgy goes from raw material to metal, metalworking turns the ingots into workable material), which means you caould, given enough time, create some raw materials yourself. The gain is minimal, since you're spending days to save a minimal amount of money, but it is nonetheless useful to explain how NPCs actually make those nondescript materials.