When first acquired (whether from drops, treasure caskets, AH, bazaar, or NPC Merchant Yoyoroon (Nashmau, G-6)), they stay in your inventory and are stackable. To transform the inventory version of an attachment to one that can be readily equipped to an Automaton, you must go see Tateeya in the Automaton Workshop in Aht Urhgan Whitegate (I-7). After you talk to her with Puppetmaster as either your main or sub-job, she will tell you to trade her Automaton Attachments (she only takes them one at a time). Doing so will remove the attachment from your inventory and add it to your Automaton's. Once the attachment is in your Automaton's inventory, you can see its actual description and choose whether or not to equip it to your Automaton.
There is no level requirement for using attachments.
You can only have one of each attachment for your Automaton.
Attachments do not take up any inventory space after they have been fitted to your Automaton.
Once fitted, attachments can not be replaced, unfitted, dropped or destroyed. You will never need more than one of each.
After you talk to Tateeya once, you do not need to be on Puppetmaster to trade her more attachments.
If you try to trade her an attachment you've already fitted, she will not take the item and let you know she has already installed it.
Attachments can be loosely grouped into "sets" of ten attachments, one for each element. The attachments can be obtained in the following ways:
The first and second attachment sets can be bought from Yoyoroon (Nashmau G-6). Attachments from the first set each cost 4,940 gil and the second for 9,925 gil each;
Most Crafted attachments are made in stacks of 12 but automatons can only be equipped with one of each attachment. Turbo Charger II and Vivi-Valve II make 3 at a time.
The Automaton Equipment screen is found in the same area as your own character's equipment menu is, however, when you have Puppetmaster as either your main or sub-job, the Equipment option gives you two sub-menus, 'Master' and 'Automaton'. As you can see, the Automaton Equipment screen is much like that of your own character. However, there are only two type-based slots, Head and Frame. The twelve other slots are for Attachments of any kind, as long as the total amount equipped meets the requirements.
Each dot and the # / # beside it is your Automaton's elemental capacity. The first number is the total charge of Attachments of that element, and the second is the total charge that can be equipped at once. Different Automaton Attachments have different charges; lower ones can be equipped in greater numbers, and those with higher charges only a few.
Your Frame and Head determine not only your Automaton's HP/MP, skillcaps, and stats, but also its available elemental capacity.