In short, to exchange items or materials in Scarlet Nexus, you first need to get past the first standby stage and reach Phase two. After this point, you will be able to access the item exchange via an option in Satori the archivist's store.
If you don't know what this is, it's the bike next to him, just walk up and hit whatever button shows up above it to enter the store. Once opened, you will be able to exchange various items by selecting the tab shown below.
This tab is the item exchange, and using it will allow you to use various materials gained out in the field to get all item types in the game. This means weapons, plug-ins, and even visuals and consumables can be purchased this way instead of money.
You can even put certain items on a wishlist, and you will be notified when you have the required amount of resources to get that item. That being said, if you want to exchange items, you will need to check what resources you will need on the bottom right of your screen when looking at an item.
But if you don't have any of the items on hand just yet, you can get them from certain enemies in the game. You can also check what items drop from certain others by looking under the enemy section under the library tab in your inventory.