The "Test of Faith" is one of the easiest but longest of the quests before joining a camp. Diego will tell you to go to the Old Mine and collect a list of supplies that the mine workers need from someone named Ian. Ask Diego why Ian would give you the list, and he will say to tell him Diego sent you (if you skip this step you will be unable to get the list until you ask Diego this question). The mine is north west of the Old Camp; if you ask how to get to the Old Mine, Diego will tell you that the local map-maker, Graham, should give you a map to the Old Mine. If you go to Graham, you can get the 50 ore map for 30 ore by mentioning Diego once, and, after insisting that Diego said you could "get" the map, not "buy" the map, you will get it for free. He also sells a Map of the colony which you probably want to get if don't have it yet. (you can view the map by pressing "m")
Just follow the road out of the main gate, across the bridge, and through the forest. You can try to swim around the forest and many of the enemies, but be careful around the Lizards further upstream. The Old Mine is fronted by abandoned wooden turrets and a masher, with the entrance behind. Sometimes, you will find two Templars, one named Gor Na Drak, walking to and from the Old Mine, and waiting at the entrance. Gor Na Drak, when asked, will teach you how to remove Minecrawler mandibles for free ore (1 skill point) if you ask him.
Once you get into the mine, start making your way down. Ian is next to the second set of red flags, the second store in the mine, run by Alberto (the first was on the starting level, run by Santino). Get the list from him and head back out of the mine.
You can return the list to Diego to complete your quest for the Old Camp, for experience and brownie-points. If you plan on joining the New Camp, you should give it to Lares at the New Camp to help you join that camp as a Rogue. The Test of Faith has no impact on the Sect Camp fortunately.