This is usually not the way to go unless you are advertising a commercial web site. Even though you don't want to pay for ad space though there are folks out there with web pages like yours who may offer to swap ads. That makes having a set of banners available useful. Very often users who enjoy your site will offer you a free link from their own web page. Someone who has similar interests usually contains these links in a review.
Reciprocation is again appropriate.
Link lists are a standard part of any web site design. Finally, most commonly and certainly most importantly, you can list your site with various search tools or search engines. This is ideal. The searcher uses these tools to find something when they have no idea what is on the web with regard to a particular topic. Many of these search tools are almost household words today.