Sometimes affiliate programs are referred to as partner programs, but they both mean the same things.
A partner program will typically ask you to submit your site details before approving your account.
Once your account is approved, you will then be able to access creatives such as banners that you can display on your site and provide you with tracking links.
For instance, Google search for the term “Lotto Affiliate Program” or “High Commission Affiliate Programs”. Once you identify a program you think will be a good fit, simply sign up and follow the approval process.