DeviantART already has some great browsing options that are really helpful when looking for new deviants. I've typically found that Popular All Time, Popular 1 month, and Popular 1 week show the same deviants over and over again, so if you're looking for more variety in deviants, I suggest browsing through Popular 3 days, Popular 24 hours, or Popular 8 hours.
Browsing through Newest will obviously give the widest variety in deviants, but it can also get annoying sifting through the massive amount of art for quality. I personally prefer What's Hot because it has a lot of quality art and shows a variety of different deviants.
If you find an artwork you like, you can also click the "More Like This" option on the artwork to get a whole bunch of similar artworks by the same artist as well as other artists. (What is More Like This?)
Now what's really cool is that you can also search the More Like This page by Artist or by Collection.
Searching by Artist shows you related artwork from different artists. With just one click, you can add the artist to your watch list, or check out more work from their gallery.
Searching by Collection shows you similar artworks in other people's Favorites Collections. You can now stalk other people's favorites to your hearts content!
New and Random Deviants
If you're feeling particularly adventurous in your quest to discover new deviants, then you can check out DeviantART's Today page, which can be found in the drop-down menu.
On the right hand side of the page, you'll see a whole list of new deviants and groups. Maybe drop by and give them a friendly hello!
Random Deviant, which will bring you to the profile page of a random deviant (duh ). The good thing about this is that it only brings up active deviants who have logged in recently. You can, of course, also click on Random Deviation or Random Group.
Deviation Thumbshare Forum
The Forums are another great place to go to discover new deviants. DeviantART has two Thumbshare Forums, the regular Deviation Thumbshare forum and the Premium Thumbshare forum. Both are filled with lots of great artworks just waiting to be discovered!
DeviantART on Social Media
I highly recommend following DeviantART on Facebook, Tumblr, Twitter, or Google+ if you love discovering new artworks. The DeviantART staff who run these accounts post a wide variety of artworks, and its definitely helped me find wonderful new artists to love!
I love browsing through the Daily Deviations because there's always a wide variety of artworks and artists that are featured each day. Most of the artists that are featured have been given their first DD, so you're always guaranteed to find an artist you've never seen before!
Features and Groups
While the Daily Deviations are the major feature on this site, there are tons of other features that promote amazing artists. You can browse Art Features in the journals or check out the Journal Portal at the bottom of the home page for popular features.
Watching groups is another fantastic way to find new deviants who have tastes in art similar to yours. Check out some Groups today!
Now here are just a few deviants and groups I've come across who create some great features!
ProjectPorkchop focuses on promoting talented, but under-appreciated artists. I've found a ton of amazing artists to watch from these features, and I highly recommend watching the group or Astralseed, who puts together the features.
All-about-features collects features in their gallery and also has a feature series called DA starters that promotes new deviants.
Daily-Lit-Deviations features several great prose and poetry pieces everyday.
Lintu47 runs a feature called dA Love for Everyone that has a little bit of everything including artist interviews, artwork features, and group promotions.
3wyl runs a weekly feature called To Be Seen which showcases the work of 5 photographers from all areas around the dA community.
techgnotic creates very interesting and beautiful features of artists and artworks.
meganjoy has some of the loveliest themed photography features I've ever seen.
OliviaMichalski features lots of beautiful and stunning photography.