In order to earn the "Back to work." trophy in Firewatch (EU), you simply need to continue through the story. Here are the steps to get there from the end of Day 1.
At the start of Day 2, once you have had your conversations, you will need to retrace your steps through the cave path which you discovered at the end of Day 1. That means turning 180 degrees when you reach the foot of your tower. Go back past the outhouse and down the rock walls, and make your way back through the cave. At the other end, instead of going left (west) back through the canyon you're going to head straight ahead (north).
Pretty soon you will see some power lines, so you should just follow those all the way until you reach the summit of a little outcrop. Report the incident you find at the end of the wire. Turn around -- instead of following the path back down to the left that you took up here, there should be a way down to the right marked by a discarded beer can which will take you west. You should pass a sign and then a log bridge. Beyond that is a bag you need to swipe from a tree. Grab what's inside, including a camera, and head past the backpack. Rappel down twice using your new ropes and continue south. The area opens up when you get to some burned trees, but just keep heading directly south back towards Thunder Canyon which you visited on Day 1.
You should come across a natural bridge that lets you hop over Thunder Canyon and continue south. After some climbing up and dropping down, you should pass the first Cache box you opened on Day 1 and then rappel down the slope you encountered on your first day when the rope broke. Shortly after, rather than continue to follow the path back to the lake, keep an eye out on your left for another rappel point. Take it down the slope and keep going south, you should pass Cache 309 on the way. Past the cache your path will start to veer from south to south-west as you navigate some dense trees. You'll get to a stream -- follow it right (west) to a waterfall. Facing the waterfall, you want to head right again and go underneath two big rocks to find an abandoned campsite. Report everything in and eventually you'll trigger the end of the day, earning your trophy.
Note: As soon as you get the camera you can earn another achievement if you use up the entire roll. A small note of caution - there are some dialogue moments later in the game that you can take advantage of if you still have film left in your camera, but you need to finish the roll completely before the end of the game.