1. Cheaply level your craft
This tip assumes you know the basics of crafting. The fastest and cheapest way to raise your crafting skill is to complete work orders given out by your crafting trainer in the Artisan district in your capital city. Crafting costs kinah (money), but there are three important things you should bear in mind to maximize your savings.
First, only grind up your skill on work orders 10-15 levels below your current crafting level. For instance, if your Tailoring is at 40, only do work orders that require a 30 Tailoring until you reach 50 skill points. Each work order will give you around 1-1.5 skill points, will complete more quickly with a higher level of success, and your extra ingredient(s) cost will be lower from the crafting vendor.
Second, only make as many items as needed to complete your work order. Each work order only requires that you create 6 items but the trainer gives you enough basic ingredients for 8. Too many people click "Craft All," which ends up wasting additional resources (i.e., money). Manually type in "6" and then press your craft button.
Finally, you will receive a random item reward each time you complete a work order. These rewards range from valuable crafting ingredients to new crafting recipes. It's usually a good idea to hold on to the extra ingredients for when you need them and sell off any recipes you don't need on the trade broker (auction house) to recover some kinah. Some of the recipes are quite rare and will fetch a nice price.
2. Maximizing your profits
The best place to make kinah is on the trade broker. That said, it isn't always the case... Sometimes people will list white items on the trade broker for less kinah than they can make from simply selling it to an NPC vendor. Strange, but true! If you find items undervalued on the AH it's always recommended that you gobble them up and resell them for profit.
Personal store items are also often underpriced so make sure to keep your eyes open. This is great when you find an item you need for a good price but even if you don't need it, you can turn around and sell it on the trade broker or to a vendor for a profit as well.
As for selling items on the trade broker, it's always a good idea to do a bit of quick research first. What are similar (or exactly the same) items listed for on the broker? Can you sell it for more to a merchant? If not, what are the cheapest few items listed on the broker? It's always a good idea to price your item cheapest unless there's a gap between the cheapest and the second cheapest items. If there's a big gap, price your item somewhere between the two. It won't sell first, but once the first one does, your item will now be the cheapest available!