You don't need to be a crafter to Convert bonded gear.
You need to be a crafter and have the proper catalyst to attach it to an item, though. Each materia has a grade 1-5. You need carbonized matter of the same or higher grade to attach the materia.
You can Request A Meld from another character. You will need to have the item, the materia, and the carbonized matter. This lets you have someone else meld your gear when it is already bound to you.
Each item has a hidden stat cap based on the item level. Adding materia cannot increase any of the stats past this hidden cap. When attaching a materia it will tell you if you are not getting the full value.
Each item has a number of open materia slots. These are the circles in the item description. Attaching up to that amount of materia will always be successful. You can try to meld more materia after that but with a very limited chance of success. This is usually called over-melding. If an over-meld fails you lose the materia and catalyst but not the item you were trying to meld to.