Well to be honest, there is no sure fire way, but I do have a few suggestions.
First, I'de just like to let you know that if you are on Tumblr just to get followers, you are on the wrong website. Tumblr is a blog to just express yourself; to have fun with pictures and phrases and not worry about being popular. The moment you think being popular is more important then being a fun person, then you have gone down the wrong track and will not fit in with the Tumblr crowd.
But basically, you have to have a good blog. It doesnt matter if you have no followers or anything, as long as you have a good blog. So that means finding the blogs that you like the best, and following them. Then start reblogging the nice pictures that go with your blog. To be honest, I have a Humour blog, so I find the funniest pictures and things that I can and I reblog them. I can reblog anywhere from 10 to maybe 70 things a day, depending on what I'm feeling. But if you're a fashion blog, then follow all the gorgeous fashion blogs and reblog the nice pictures. The person who you reblogged it from will know, and they will check out your blog. If you listened to what I said and have lots and lots of gorgeous pictures from all different places, that person will follow you. And that starts a chain reaction, because when you reblog something from someone else, they will see your beautiful blog and follow you as well.
But honestly, there is absolutely no way to get followers if you do not have an active, nice blog. Thinking that people will just follow you because you ask them to will not work. You can only try and hope for the best

Lastly, here are some good blogs.
Gorgeous Blog:
http://heyrainbows.tumblr.com/Food Blog:
http://ffoodd.tumblr.com/Hilarious Blog:
http://bitchslappedbro.tumblr.com/Pick Best Answer?
Thanks
