I've been pretty lucky with getting Trader Sam's reservations. You can also try in person to get in; I've been able to do that without a reservation. It's a lot easier if you don't mind being outside on the lanai, which is very nice unless you want the indoor interactive experience. There's a walk-up bar outdoors and you can sit on the Tangaroa Terrace side; you still get the tiki torches and sometimes live music from an island band.
As Bunkie said, there are dining notification services you can sign up for that will alert you when a reservation comes open for the date/time period you enter (breakfast/lunch/dinner), but you have to be pretty fast to grab the popular ones. I've been able to get Trader Sam's that way. I just use the free version but usually miss 3/4 of them. It helps a lot if you're logged in to dining and can quickly check. You're able to set several alerts at a time (6 I think in the free version). The alert will tell you the date and time period when a reservation has come open so you have to rush to the Disney dining res site and try and grab it. I generally set 2 alerts each day (lunch and dinner) for the days I could use for Trader Sam's.
Good luck!