I believe the official season starts in November and ends in February. Tickets aren't too difficult to come by, and not very expensive compared to MLB tickets.
Here's a link to the Licey website.
http://www.licey.com/ There's some info there.
Idiot in hindsight story: I was in Santiago in January and decided to hunt for some Dominican team beisbol t-shirts around town. Could not locate any around Calle de Sol, so my friend takes me over to Estadio Cibao, because Licey was playing Aguilas. He works for a newspaper covering sports. We get there and the stadium is closed, but he speaks with a couple of security guys and they let us in to buy some t-shirts. Could've gotten tickets and watched the game, but no, I'm not thinking. The game turned out to be really good. Kicking myself in the *** since then. I'm at a game next season.