Fallout: New Vegas

I have written 2 solutions first has no spoilers the second one does.

1st Solution

This is story related and cannot be missed. Select the new mission you have once you start the game with the dlc loaded. Follow the mission. There are way points to follow and people to speak to and your pip boy to help you out.

2nd Solution *SPOILERS* (kind of)

When you start the game you will hear a radio broadcast looking to recruit someone to help with their caravan. This will show in your pip boy and the quest is called Happy Trails Expedition. There will be a way point directing you to go to the northern passage. If you have already found this location you can quick travel there if not quick travel to the nearest place and hike the rest.

Once there you will have to talk to Jed. He will explain about the caravan and what they are doing. He will then tell you, you need to be carrying 100 pounds or less of stuff. There is a chest next to him to stash what you don't need. Once that is done talk to him again and tell him you are ready to go. There will be a loading screen and then some dialog. During the dialog the achievement will pop.

The next achievement you are going to get is Restore our fortunes - Resupplied Daniel and the sorrows

Very straight forward Achievement.
Once you load up the game after downloading the DLC. You will get a notification saying that there's a radio broadcast coming from somewhere in the north. Go to Northen Passage, enter, speak to the old guy and he'll tell you that there's a "weight limit" of 100. Just offload the stuff you don't need in a box to the side of him, you can retrieve your stuff once you finish in Zion. And once you have under 100 in weight. Just tell him you're ready to go and BOOM! 20 gamerscore!

ok this is very straight forward all you have to do is start the first mission of the dlc which gides you to its location when you get asked to get rid of some items to put a limit of 100 on your weight if you have got the right perks you can get around dropping your weight to 100 by saying i can carry all of my stuff your stuff and the stuff the brahmin is carrying. once you have said this you will leave for zion the second your game has loaded the achievement will pop