Bounty Hunting:
The goal is to collect Bounty Vouchers.
Destroying any ship with a Wanted tag will net you a bounty voucher with the value of their bounty, redeemable at any station in the system that issued the bounty. Ships can have bounties in multiple systems, but only the bounty issued in the system they are in presently will show when you identify the ship. Using a Kill Warrant Scanner on them in normal space will "reveal" any additional bounties on that ship, and you will likewise be awarded those bounty vouchers upon the destruction of said criminal. Once you have identified, or identified and KWScanned a wanted ship, you can view the value of their bounty by selecting them in the contacts section of the left hand menu.
Wanted ships can be found:
in SuperCruise in the system, you can interdict them or allow them to interdict you.
In Nav Becons and Compromised Nav beacons (Compromised Nav beacons will have more difficult, higher reward opponents)
Resource Extraction Sites, or RES zones. These will come tagged as normal (RES), Low-Intensity, High-Intensity, or Hazardous. Much like the Nav Beacons, the High and Hazardous RES zones will have more difficult, higher reward bounties. Also, Hazardous RES zones will NOT have a local security force. You are on your own.
Unidentified, weak, and strong signal sources are also spawn points for wanted ships. Like the previous examples, they scale in difficulty.
Earned bounty vouchers will show up in your transactions tab in the left hand menu. They will specify in which system/faction the bounty can be collected. Once docked in a station controlled by the faction specified in the dialog in the transactions tab, go to the "contacts" section of the Starport Services menu, and you should see a display of all Bounties redeemable at that station.
Combat:
Mercenary work is done by turning in Combat Bonds
Combat Bonds are earned in Conflict Zones. These come in Low-Intensity and Hi-Intensity varieties. The biggest difference, so far as I can tell, is that Hi CZ's tend to spawn more ships, and occasionally capitol ships. Low CZ's are less populated and more survivable. I prefer Low CZ's if I'm trying to farm credits. Hi-CZ's are more of a thrill, but you get shot up faster.
Enter a conflict zone, go to the right hand menu, and then the functions tab. On the "Faction" line, you will be able to choose a side in the conflict. You MUST do this, otherwise you will NOT be awarded Vouchers for ships destroyed in the zone.
Once you have chosen a side, allies will be green, enemies will be red. Shoot the red.
Return to any station in that system to redeem your Combat Vouchers. Like with Bounties, go to the "contacts" section of the Starport Services menu, however you need to go one option down on the left side to redeem combat bonds.