This page in our guide to Control will show you how to get materials and source.
Materials are items that you can use for crafting to create new mods, improve weapons, or create entirely new weapons. There are a lot of materials in the game - they come from specific cases often hidden in extra rooms or hard-to-reach places.
Some of the materials can also be obtained during missions, both side and main. Moreover, you can "grind" materials by completing Board countermeasures, where often the rewards are materials.
As for the source, it can be treated as currency we spend while making a mod or improving/crafting a weapon. The main way to obtain source is to kill enemies. As before, it is worthwhile to complete Board countermeasures to face new enemies and challenges and obtain valuable materials and source.