Welcom, Casinofatcat!
Most affiliate programs will bend over backwards to help you market them as efficiently as possible if you contact them and ask for advice. If they don’t – they aren’t worth your trouble anyways.
The most important way to market in this day and age is SEO – search engine optimisation.
Learn as much about it as you can – the web is full of informational sites and message boards regarding this. Optimize your site as best you can. That will give you a good start.
If you run into trouble or have questions, ask in the Seach engine section of this board. There are a number of people who will give you excellent advice.