You can, if you want to make the effort, level a craft starting with less than 1 gold and end with more money than when you started. This is without farming for materials, just buying off the TP. Here’s what it will take:
1. Patience. You can save significant amounts of money by buying with offers instead of buying at the seller’s prices. But doing so takes a patience, because an order may take an hour or even a day to fill. And it may not fill at all if you get the offer price wrong.
2. Research time. Most people make everything from raw materials, but it’s often cheaper to buy some parts or refined materials from the TP (with offers). Right now, there are a lot of masterwork parts for sale far under the cost to make them, because of the Monthly masterwork crafting requirement. You’ll need to compare raw materials, intermediate materials, and part costs to determine which avenue is cheapest. You can use sites like GW2Spidy, but their prices lag the TP too much for me.
3. Karma. With Karma, you buy recipes to make rare item parts. The Rare recipes make parts for Level 35, 50, and 65 rare items. While Fine and Masterwork items rarely sell for a profit, you can usually find one or two rare ones that give a decent profit, but exactly which ones are profitable changes fairly quickly. If your goal is just to level up cheaply rather than actually make money, you can sell at or near your cost (but remember the 15% sales fee!).
Keep in mind that the road more travelled will be more expensive, because the other travellers drive up the cost of materials and low the prices of whatever you sell. So, I’d avoid using a guide.
Good luck!
