Hello Xth Squad,
It's actually pretty easy, and cheap, to boost items. You go to the Hinowa Academy, then Development Lab, select Development and then Boost and then pick the item you want to boost from either your inventory "sub-disk" or "member" if it's currently equipped. It'll show the equipment in a screen on the left side and there will be a screen on the right side that shows "Before" on top and "After" on the bottom with the "Before" section showing what materials you need to boost the item as well as the cost.
The above is relatively self-explanatory, however, I actually wanted to explain something that I believe the game only shows briefly on a loading screen and somewhat buried in the Information Terminal - Squad Handbook - 19-E: Development Tips area and that's how much you can boost items.
Every item has an item level and that level is not only the Blood Code level needed in order to equip it but also the number of times that particular item can be boosted. For example, a Longsword is level 2 therefore you must be level 2 to equip it but you can also boost it up to 2 times for a Longsword +2. I say up to because a single boost can add more than just +1 each time.
Hopefully this helps someone out.
If there is anything I can do to make this solution better please don't hesitate to let me know.