How Do I Get Other Websites to Link Back to My Blog?

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Hi! I'm really trying to develop my blog so I can earn an income while staying at home to raise my three girls. That said, I'm doing a ton of research on how to maximize Google AdSense revenue. What I'm learning is that blog owners earn more per click from their ads if their blog has a good page rank. With my limited understanding, I think that means Google will give me better paying ads if my blog is linked with multiple credible sites. So, in addition to registering my blog with various directories, I learned it was important to get my blog linked to forums and other blogs. Now, I'm finally getting to my question! How do I do that? I googled "how do I add my link to forums" and it wasn't very helpful. I also googled "parenting forums" because my website (believerinbalance.blogspot.com) is my attempt to share humorous experiences from my life that others moms can relate to. I was able to add a link to my blog to cafemom.com, but that's it. I have seen several websites offering to do a link exchange, but the ones I looked into worried me a bit with their content. Can somebody give me some advice on how I can get other websites to link back to my blog?