If you never advanced with the RV before it's explained pretty well here:
Basically all you have to do for this achievement is use the RV.
Not explained in the guide above is where to find fuel.
A very good and consistent spot is the construction sites (the unfinished houses). Basically you want to look for giant oil drums (metal barrels) or red fuel canisters, either of these can be represented by the oil drum on the mini-map.
Other good spots include garages and inside of gas stations.
Now I don't know what triggers the mission to advance but it should pop up after a hour or so. Just play normally, upgrade your base and do missions. Then you'll find the green "?" on your map somewhere for the "Gotta be a way out ..." mission.
Don't forget you'll need to collect five rucksacks of fuel and you also may need some supplies (in your management menu the icon of boxes to the left of where your fuel is displayed) in case of broken tires on the RV. You'll need exactly 25 units of fuel and I think it's four units of supplies per tire. Not sure if it's possible for all four tired to be flat but I'd have 16 supply units just in case.
I also just found out that the engine can be busted which will require 20 units of supplies and five units of fuel and then take 30 minutes to repair.
Depending on your what level you're trying to advance to and from can effect what you need.
Needing fame is another possible resource that may be needed to repair the RV.
Please read the comments from a previous years guide I wrote for more info about these two things:Solution for Starting Over in State of Decay: Year-One