1. Enter the Vikki and Vance Casino and talk to Johnson Nash, who will give you the quest.
2. Enter the Bison Steve Hotel. There will be 2 or 3 convicts either in the lobby as soon as you enter or in the hallway just ahead. To the right is a locked door that can be opened via the terminal next to it (science 25). Inside on the table is the key to the maintenance door which can be used to get to Beagle. Alternatively, if you have lockpick 25 that can be used to pick the maintenace door.
3. Make your way through the bottom floor, killing all convicts along the way, until you reach the maintenance door. If you have either picked up the key, or have the ability to pick the door, do this and go through the hallway to where Beagle is being held. Otherwise simply go through the large open room where the other convicts are waiting. There will be 1 or 2 convicts in the room where Beagle is being held.
4. Upon killing these convicts, it is very likely that the 3 or 4 convicts in the large room and the convict leader (who carries an incinerator) will attack you. If you free Beagle before fighting them, he CAN die. If you do not free him, they will not attack him.
5. Regardless of whether Beagle is alive or not, you can retrieve his notes, which are needed to continue the main storyline. If he is alive, you can decide whether or not to simply leave, or clear out the Bison Steve completely.
6. (OPTIONAL) Take the stairs up to the second floor, or repair the elevator (repair 25?) and clean out the hotel of all convicts. There are also 2 or 3 convicts outside on the roller coaster. If you do not kill them, they will just remain there forever.
7. Talk to Johnson Nash about getting a new sheriff for Primm. He will suggest an NCR officer, and Meyers, a former sheriff at NCRCF. You can also use Primm Slim, located just insicde the casino.
8. NCR- Travel to the Mojave Outpost, talk to Major Knight and either pass a speech check (20 barter) or complete a pair of relatively short quests.
9. Meyers- Travel to NCRCF. Unless you have completed the quest Run Goodsprings Run, everyone there will attack you on sight except for Meyers, so a stealth boy is a good choice, or powder ganger faction armor, or simply go in guns blazing. Just make sure not to shoot Meyers. Talk to him, and then head to the Mojave Outpost to talk to Major Knight about giving him a pardon (200 caps OR speech 30)
10. Primm Slim- Talk to him and tell him he could be reprogrammed (science 30 OR 3 fission batteries and 4 conductors).