Metro has released a schedule for it’s late night rail and express bus service in LA on Friday and Saturday nights: http://www.kcet.org/updaily/1st_and_spring/transportation/metro-releases-late-night-train-service-schedule.html
The good news is trains run more frequently, and later than expected. Subway trains leave downtown every 10 minutes (alternating between Red and Purple Line trains) until 2:12 a.m., and Gold Line trains run every 20 minutes in both directions until 2:12 a.m. Check the Metro schedule for specific info about each line (links to individual schedules are also in the article above).
While running trains this late is a welcome step, why not keep them running 24 hours? The last Red Line train arrives at the North Hollywood station at 2:41 a.m., but the first train of the next day leaves at 4:31 a.m. If Metro were to offer trains once every 30 minutes after the last train, there would only be 4 additional trains required. I would think the cost of operating those trains (which could be the short 2-car trains) would be mitigated by the public good that could result from non-stop public transit service.