This has been the best book I've read on Bioinformatics Algorithms - the perfect mix for someone with a CS background that wants a deep look into how mathematical concepts are applied to biological data:
What you should know would depend on which aspect of bioinformatics you're interested in. As a CS-trained person, you may need to be able to communicate with people coming from the bio side of things. This means acquiring domain-specific vocabulary and a basic understanding of the questions you'll get to work on. You should probably start with a biology text book if your knowledge in that domain is limited. At the moment the big thing is high-throughput sequencing and human genetics, so Devon Ryan's comment is a good starting point. However, depending on which environment you end up in, you may not need to know much to start with and may pick things up as you go.