***MINOR SPOILERS***
Start Wyatt's chapter by selecting his picture from the bulletin board that serves as the DLC's menu screen.
From here, just play through the chapter as you would any other chapter of TWD - it takes no more than 10-15 minutes or so.
The most difficult part for me came at the end, and exactly what it is will depend on whether you stayed in the car or not. If you left the car to investigate, there will be a point where you need to shoot at zombies in the fog. The fog gives you a reduced period of time before you can move over and shoot at them. Even still, this shouldn't be all that difficult.
If you stayed in the car, your pursuer from the beginning of the chapter will find you, and you will go through a series of quick-time events. Again, this is harder than everything else in the chapter, but it's not exactly difficult.
Whichever path you take, once you complete either the quick-time events or the shooting, the achievement will unlock.
At the mid-point of the chapter, try and convince Eddie to go out and investigate himself, and you will trigger a game of Rock-Paper-Scissors, which you can attempt to win for the "Two out of Three" achievement.