This has changed over the years since I've been on Wattpad.

Before, you had to email Wattpad directly with a request to have your story included. At that time, it was almost like a pitching contest with the hope they would like it enough to want it included on the coveted list. Once they accepted the request, a 'rep' at HQ would reach out and assist you throughout your tenure while it was on the one and only Featured List. This is what happened with TWO THOUSAND YEARS, though I waited months for the response, which happened not soon after it won its Watty in 2016.

Now, there is an actual form that one can fill out to request being featured on one of Wattpad's numerous 'Wattpad Picks' lists. The requirements from Wattpad are specific, however. This is taken directly from their FAQ page:

If you believe your story has what it takes, you can fill out an application to be reviewed by us. Your story can have any number of reads, votes, or any other activity and still be eligible! Here's some criteria that we're looking for:

—Compelling stories that appeal to readers, and have their own distinct voice, style, or spin. Something you can't put down!

—A degree of care and quality, free of obvious typos or consistent grammar errors that make it difficult to read.

—Minimum 10,000 words to submit, or must be a completed short story or poetry collection if less than 10,000 words. Make sure you mark your story as Complete in the Story Details section.

—The same story cannot be submitted more than once within 3 months. However, you can apply with multiple stories at the same time.

If the story is ongoing it must demonstrate a consistent, reasonable update routine.

—Stores in the Random category may not apply.

—You can only apply with your own stories and cannot nominate another writer.

Individual applications will not receive responses. If you are selected for promotion, you may be notified through private messages or through your notifications. Note that while the application puts the story in front of us, we may still promote stories that haven't applied if they meet our criteria.

That form can now be found in the external link of this chapter. 

If your story is picked to be featured on one of the Wattpad Picks lists, you'll see it added by WattpadExplorer to one of the reading lists, and the rest is history!