look at what your competitor is doing and try to copy that.

Agreed with @high_plains_drifter, in these days Reverse Engineering Your Competitor's Backlinks is the best strategy, use ahrefs pro tool for getting idea how your competitor creating backlinks or use my service i am providing on fiverr check out my signature, if you need any more information please ask.

For a website like that, your best way to promote is Social Media. People don't search for memes on Google, do they?

Build back links to your humor website from entertainments and related web sites, directories, social sites, etc. Social sites would be a good start to increase traffic.

Using humor is a new tactic. I found several these guys are using> I really like this one. They have another one that's about Bigfoot.
http://vehiclewraptalk.com/tag/vehicle-wraps-on-mars

Hi,
Hope you are doing well. As I believe that Guest posts are known to be the best way to attract more and more readers to your website and it is imperative for it to be interesting and attention-grabbing. We understand what it takes to create a highly attractive guest post that would bring you a large pool of readers, hiking your website traffic in a few days.

Thanks!

[DELETED]

Imagine that you are a fan of the site. What would you do as a fan?

You might have a blog and tell your friends and followers about a funny site you found. *Do guest blog posting.

You might link to the funny site directly from your blog or website. *Ask or barter with a website owner to create a link to your site.

You'd share the funny images and other content on social media. *Share your content and encourage others to do so.

Lesson: Always put yourself in the shoes of your customer or follower. That way you'll better understand things. It will also help to keep your behavior 'natural' for Google.