Only one "official" option available really - sign up to become an "All Red" member (£29 per year). Then on the morning when the tickets are released to members, be ready to hit redial again, and again, and again ...until you eventually get through.
your best bet is to try an away game. if you can sit on your hands should they score, go for a home stand as i doubt you will get an ticket in the away end without being a club member, season ticket holder etc...
Check whether there are any local supporters clubs where you live. There are quite a lot throughout the country and they get allocated a number of tickets.
Try Carling Cup, I can get extra tickets (on top of fancard ones) to the early rounds that Liverpool play. You could have probably got tickets to yesterday's game too.