There are two main ways to level up crafting in FFXIV: ARR, which are Tradecraft guildleves and completing the crafting log. By using these you don't really need to grind your levels by making lots of useless items; however you can still do that if you want to.

The thing with guildleves and the crafting log is that they are limited. You will only gain 8 guildleves per day and they are shared with battle classes. It is better to keep these for leveling crafting and using one of the many other methods of leveling your battle classes. You can store up to 99 guildleves so you are not forced to use them or lose them every day.

The nice thing about crafting guildleves is they give a lot of EXP. The level 10 guildleve to the left will earn you 3872, plus they give you shards which you will use in crafting other items. Unlike in 1.0, you are not given the crafting materials needed to do the quest.

The way the crafting log works is that the first time you craft a recipe you will be given a bonus EXP reward, so by crafting everything in your log you will earn some nice EXP. But as the bonus is only on the first synthesis you will run out.

The alternative is old school grinding, which is very repetitive and boring, so we feel it is better to level up crafting at a slower pace entirely by guildleve and crafting log rather than this way. Hardcore players will tell you otherwise however, and that is the road to riches if you are playing on a fresh server. Being at the top of the leveling path is very rewarding, until you hit the cap and lots of people catch up.

If you do go down this route then you need to research which recipes will result in the lowest cost and use the least amount of materials. You will end up losing lots of money as you will end up selling your finished products to an NPC since players will not buy them fast enough.