The process of apprenticeship is an important one for any Craftsman. It is when they come under the tutelage of someone (ranked Professional or higher) and learn the necessary skills of their trade. The first step involved is finding someone to be your master (we use that phrase throughout, though again it doesn't indicate rank in the Guild just that they are a teacher). This is something that should be considered carefully, since you want to match up the skills they have with the ones you want to learn. For example, someone who doesn't work with metal can't teach you to work with it either (for purposes of crafting, etc.).
It is up to you to convince them to teach you, the onus is -not- on the master to take a student. It is one of the things necessary for promotion in the guild, that may add some incentive. There is no fee required, and no prospective master can require one, but you are free to offer it to give them a bit more reason to take you on. One thing that may help of course is approaching them ICly instead of OOCly about it.
The learning of the skills involved can be a fairly involved process however. Learning to work with metal and forge it into the right shapes is not a short one, and can involve a great many details. A good master will teach the student how to find materials, work them, sell their goods, etc. There are many things that go into the process, and apprenticeship can often take a good while. On the downside, that may mean that there's quite a while between being a Petitioner, and being a Professional in the guild. However, this does mean that there is a lot of potential for interesting roleplay.
An apprenticeship often will culminate with some sort of apprentice piece, an item or display (specific to the discipline such as blacksmith, tailor, guard, etc) that shows the apprentice has truly gained some grasp of the necessary skills. At this point they are usually promoted to Journeyman status. They may take a more active roll in running a shop, sellling their own wares for their own profit, as opposed to the profits going to the master. This is a time to hone their skills and learn something about the world of business and about practicing their chosen craft. As with the apprenticeship, the Journeyman stage often ends with a journeyman piece of some sort that displays how far they have come.