Like others have said before me, self-promoting yourself is probably the biggest way to get more potential buyers to look at your gigs!
You can promote yourself on tons of social media sites such as Facebook, Twitter, Instagram, Tumblr, ect.
Using #hashtags that are relevant to your gigs allow people you don’t know to find your gigs.
Another good way to help get exposure over social media sites is to have your friends/family/acquaintances share your fiverr page. You could even start a specific page just to advertise your fiverr gigs!
Fiverr even gives you a clickable badge that you can place on your blogging sites and whatnot. Just go copy the code for the badge and place it where you want it. The badge code is under “Promote Your Business” in the Selling column of your options. (I hope that made sense, haha.)
Once you sell your first gig, you can encourage (politely) for your customer to give you a rating and review, and if they would recommend your service to others, to share your fiverr with their friends and family!
Giving your best and then some for your customers will also help you acquire repeat customers that are more likely to share your work.
Hope this helped!