Removing a wanted status, generally:
1. Small infraction, e.g. shot a clean ship but didn't kill it?
Jump out of the system, check bounty status on Transaction panel; usually the time remaining will be around 8 minutes. When the timer reads "On H-Jump", you can go back. Your minor bounty is now a fine you can pay at any station in that system.
2. Major infraction; e.g. you killed a clean guy?
The timer will show a bounty lasting just under one week.
Don't panic. Leave the system. Park and settle your affairs- collect what bounties you can, etc. Because you're about to die.
Buy a super cheap ship. Sidey is cheapest, but get whatever you want. DO NOT BUY A KEELBACK AND EQUIP AN SLF, unless you hate your pilot. But that's none of my business.
Fly back to the system that wants you dead. Let it kill you- specifically, go to a station and let security ships scan you. Then let them kill you. Crashing isn't good enough. I don't remember if self-destruction is? Just let the cops kill you, to be safe.
Your wanted status is now gone, and your bounty is dormant, meaning only that fresh infractions will add the dormant bounty to your total. Rebuy your Sidey, fly back to your good ship, and go on with your day.
Dormant bounties also last one week, but are not a big deal.
07 CMDR