All art submissions appear instantaneously on the artist's user page. This personal gallery is viewable by the public but is not included in the main Art Portal listings.
Inclusion in public galleries is based on a community scouting system. Once an artist submits four works of art, that artist can then be scouted by an established member of the community who will vouch for the quality of their work. Once a scouting invite has been offered and accepted via the NG Private Messaging system, an artist's work will appear automatically in public listings and searches.
Once scouted, an artist has the ability to scout others. Artists CAN lose this ability if they exercise poor judgment. Artists can also be de-scouted if they submit bad art, and can be permanently banned if they break the rules.
This is explained in much better detail in Ornery's Handy Dandy Scouting Guide.