The Shop (represented by the little shopping cart button on the top of your screen) is where you can spend your hard-earned Credits and acquire new parts for your robots.
When you open the Shop screen, on your right-hand side you can see all of the available parts in the Store Inventory. You can use the same filters present in your Inventory to sort through the different types of parts.
When you want to purchase a new part - click on the part to select it, then click the Buy button and confirm your decision in the pop-up window. In the left-hand Shop screen, you can sell some of your old parts when you find them no longer necessary.