Feel free to speak to anyone else around you if you'd like (though those conversations won't be covered here). The terminal building is rather clearly sitting there, waiting for you to enter it. Once you're within the walls of the airfield (which should happen easily, so long as you're not on bad terms with the NCR, in which case you may not be able to complete this task at all), you'll want to seek out the gigantic terminal to the right of the entrance. This old, abandoned Air Force base is where the message you're carrying ultimately needs to be delivered. But ultimately, your goal is to reach the McCarran Airfield, renamed by the NCR folks as Camp McCarran.
You can feel free to speak with anyone you run into, however. As you work your way southward, you'll likely run into the NCR Sharecropper Farm, but not much else. This area, which is one of the more metropolitan locations on your map, shouldn't have too many (if any) enemies to deal with. Once out on the Wasteland, you'll want to head in a southeasterly direction towards Camp McCarran, which should have appeared on your map after accepting Alice's offer.
