How do I collect a bounty in Elite: Dangerous?

When you destroy a wanted vessel, you receive a bounty voucher valid in one or more jurisdictions (it could be general like "Federation", or a specific minor faction like "Achenar Empire League"). To collect on this bounty voucher, dock at any station in the system you earned the bounty in, and go to the "Contacts" menu in Station Services. From there, go to the Local Security Office to turn in your bounty claims, and receive credits.