BBC have a wonderful archive of his poems and songs which includes them being performed by a wide range of people. Alternatively find Eddi Reader’s CDs where she’s singing Burns songs – they are wonderful to listen to.
Or you could download the iPhone App of his poems and songs for free! It’s been created by Scotland.org and you can also get more information on Burns Night on their site.
If you fancy a book then try “A Night Out With Robert Burns; The Greatest Poems’‘ by Andrew O’Hagan who’s done context and a nice editorial around classic Burns poems.
For more on the man himself try SCRAN’s Burns site as a starting point.