They Went That-a-Way
"They Went That-a-Way" is the third Main Quest in Fallout: New Vegas, marking your departure from Goodsprings to pursue the individuals responsible for your attack. This quest guides you towards Primm, where you'll encounter new challenges and learn more about the state of the Mojave Wasteland.
After leaving the Lone Wolf Radio trailer, head east to return to I-15, then follow the road south towards Primm's outskirts. As you approach the town, an NCR Trooper will stop you. He will inform you that Primm is in a difficult situation, plagued by raiders and a splinter sect of convicts (unaffiliated with the Powder Gangers), compounded by NCR manpower shortages.
The NCR Trooper will suggest you speak with Lieutenant Hayes. Continue west onto another road and follow it south into a makeshift NCR camp, where you'll find two tents. Enter "Lieutenant Hayes' Tent" and speak with the officer. He will explain the NCR's troubles and confirm that convicts have taken over Primm. The NCR will not be able to offer significant assistance. To reach Primm's Mojave Express office and learn more about the assignment that led to your shooting, you will need to deal with the convicts yourself. Before leaving, consider looting the tent as much as your Sneak skill allows.
Backtrack north until you find a bridge leading to Primm, which crosses over I-15. Cross the bridge, being cautious of Frag Mines placed by the NCR. Proceed to clear out the Escaped Convicts occupying Primm.