Please refer to this (modified) schematic diagram from the crew's Ascent Pocket Checklist for this discussion.
The blue shows the parts of the plumbing still filled with LOX after MECO. The green is the helium pressurization line.
Two minutes after MECO the onboard computers start the dump by opening the LO2 Manifold Pressurization Valve (1), the LO2 Prevalves (2), and sending a LOX DUMP command to the SSME Controllers (SSMECs), which respond by opening their Main Oxidizer Valves (MOVs)(3). (The Orbiter's hydrazine-fueled Auxiliary Power Units (APUs) must still be running to perform a nominal dump since the MOVs require hydraulic power to operate. This is a major reason for performing the dump soon after MECO so that the APUs can be shut down ASAP).
The subsequent flowrate and thrust profiles looked like this:
(Note these plots show total numbers, divide by 3 for per-SSME numbers).
The valves stay open for two minutes, then the onboard computers terminate the dump by closing the LO2 Manifold Repress valve and sending a TERM SEQUENCE command to the SSMECs, which respond by closing the MOVs.
1988 STS Press Reference Manual: Helium, Oxidizer, and Fuel Flow Sequence