I have had success using Tumblr but you really need to treat it as it's supposed to be treated. It's not the kind of place where you can just whack up affiliate posts and expect to get away with it. Tumblr does not like affiliate links, ads and self-promotion. They have a large audience of horny men that are looking for some great adult content. It might only be pennies at first, but as your follower base grows you will get the more traffic to your other web properties.
How to get tumblr followers? The best way is following accounts/blogs in your niche, I am sure many tumblers will follow you back if your blog content is good. You type in „big breasts“ into the Tumblr search and then click on notes and follow followers of other blogs in your niche. They will not follow you and they won’t click on your links if you spam them with posts like "Reblog my posts" et cetera. It takes some time to build up followers, but the benefits far outweigh having a fake high follower count simply to look cool or massage ones ego. And there are really only 2 rules of interacting, don't be an asshat, and don't whine/beg.
Use it to drive traffic to your own blogs. Make the sales from them, not from Tumblr itself. You can get a plug-in for WP that adds a share button to the post images allowing visitors to share the pic on Tumblr too, that can draw in a lot of traffic when the right person with a lot of followers picks it up.
I've been saying it for a long time but I'm gonna say it again, affiliates need to get back to BLOGGING, rather than just SELLING. That's the secret to building a good following, whether you're doing it on Tumblr or your own WP blog.
Too many affiliates are what I call "drive-by". It's like yelling your sales pitch from a passing car. Stop, talk, persuade, convince and sell.
Retailers know that it's MUCH easier to sell to people who are engaged with you and your site/business than it is to try to sell to passing visitors.
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Feel free to post your tips, thoughts and questions.