When first purchased (whether from AH, bazaar, or NPC Merchant Yoyoroon (Nashmau, G-6)), all attachments have a similar description: " A [some element]-based automaton attachment". They stay in one's inventory and are stackable. To transform the inventory version of an attachment to one that can be readily equipped/unequipped to an Automaton, you must go see Tateeya in the Automaton Workshop in Aht Urhgan Whitegate (I-7). After you talk to her with PUP as either your main or sub-job, she will tell you to trade (she only takes them one-at-a-time) her Automaton Attachments. 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.
You may equip attachments at PUP01.
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 1 of each.
After you talk to Tateeya once, you do not need to be on PUP to trade her more attachments.
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.