In the PC version, you must have the DLC files active from the launcher to play.
After the DLC is installed, any game you start, or save you load will trigger an in-game message about the DLC. A radio track will be added to you Pip-Boy, and a quest to investigate this messsage will be started.
You can only play the DLC packs before making the final choice for the story to ally with an specific faction at the final battle.
Every DLC pack takes you to an entire set of new locations, where you will not be able to come back to the Mojave until you finish the main quest of the DLC. After finishing the DLC, you can return to Zion and the Big Empty (locations of the Honest Hearts and Old World Blues packs, respectively), but not to the Sierra Madre (location of the Dead Money pack).
Be aware that, when starting Dead Money, all your equipment will be confiscated, to be returned only after you return to the Mojave. In Honest Hearts, there is a weight limit to how much equipment you can carry, and Old World Blues has got no restrictions.
Your companions can't follow you to any of the DLC locations.
Each DLC pack you install will raise the maximum level by 5, and add new perks.
Each DLC pack has their own ending slideshows, according to the decisions you have during the gameplay. These slideshows will play when you leave the DLC location to go back to the Mojave.
In September 20th, a new DLC pack, Lonesome Road, will be released. It has been confirmed that it will also raise the level cap by 5, you will be able to return to the DLC location, your equipment will not be stripped and your companions won't follow you.