Have you been to an art market you loved? That's the best starting point! Find details about the past event on Google including the event organizer and their social media handles and start following them to be in the loop on future events they host. (Some of the bigger event organizers have an email sign up on their website for vendors to be notified when they're taking applications.)
Go to an art market as a shopper and pick up business cards from all of your favorite vendors. Then start following them on social media to see what events they vend at! This is how I hear about 90% of my art markets. It's the easiest way to get in the loop, and start making small business friends!
Google your local Art Centers, Museums, and gift shops to see if they participate in or host any public markets.
The most important step you can take before signing up for an art market, is to identify your ideal customer. You can find all of the art markets and craft fairs in the world, but if they're being put on by your local church and you sell punk band t-shirts you probably want to pass.
Here are some different types of vending opportunities to get your brains flowing and figure out what's right for your business: farmer's markets, vintage flea markets, music festivals, fine art fairs, church fairs, vegan festivals, pride festivals, etc. Think about which event your ideal customer would attend, and that's where you should go!
What works for me might not be the best fit for you, but I will share with you my personal list of New England (mostly Massachusetts based) events/organizers I constantly have on my radar when looking for vending opportunities. Feel welcome to check them out and apply to their future events!
New England Open Markets, Boston Women's Market, Somerville Flea, Providence Flea, New England Vegfest, A little Bazaar at the Mill No. 5, 4GoodVibes, Burncoat Center for Arts and Wellness, Salvage Angel, Greenway Open Markets, SOWA, and Pride Festivals (I just google the city I want to go to and find their festival dates)