What are artists?
Artists in e621 represent the people who created a piece of art. Originally tags were used to describe artists (and they still are), but in many ways tags are insufficient. You can't tie a URL to a tag for example. You can fake a hierarchy using tag implications, but in most this cases this is excessive and leads to an explosion of redundant tags. For these reasons, artists were elevated to first class status in e621.
How do artists differ from tags?
For starters, artists can have URLs associated with them. These come in handy when you're uploading a post from the artist's site and want to auto-identify it; e621 will query the artist database for the URL and automatically figure out who it is. It isn't foolproof but as the database gets more artists, the more reliable it becomes.
You can also organize artists more. Doujin circles can be represented as artists and can have group members. Artists can also have multiple names associated with them and notes for extraneous details.
How do I search for artists?
Start at the index. In addition to browsing through the entire artist list, you can also search for artists.
By default, e621 will search across names, other names, and group names using exact string matching. You can do wildcard searching with "*". For example, searching for "bol*" will return any artist whose name starts with "bol".
If you only want to search the name field, prefix your query with name: like name:john. group: and other: work similarly.
Suppose you know the artist's homepage, but can't figure out their name. Simply search for the URL (beginning with http) and e621 will return any associated artists.
How do I create an artist?
First off, go here.
You'll see five fields. Name is self-explanatory. Other Names are for any miscellaneous names or identities the artist has, comma delimited. For example, you can place the artist's name in kanji or kana in this field. Group is the name of the group or circle this artist belongs to. Notes are for any extra tidbits of information you want to mention (this field is actually saved to the artist's matching wiki page on e621).
The URLs field is a list of URLs associated with the artist, like their home page, their blog, and any servers that store the artist's images. You can separate multiple artists with newlines or spaces.
Are artists in any way tied to posts or tags?
No. If you create an artist, a corresponding tag is not automatically created. If you create an artist-typed tag, a corresponding artist is not automatically created. If you create an artist but no corresponding tag, searching for posts by that artist won't return any results.
You can think of the artist database as separate from the tags/posts database.
This is an intentional design decision. By keeping the two separated, users have far more freedom when it comes to creating aliases, groups, and edits.
When I search for a URL, I get a bunch of unrelated results. What's going on?
Short answer: this is just a side-effect of the way e621 searches URLs. Multiple results typically mean e621 couldn't find the artist.
Long answer: when you're searching for a URL, typically it's a URL to an image on the artist's site. If this is a new image, querying this will obviously return no results.
So what e621 does is progressively chop off directories from the URL. http://site.com/a/b/c.jpg becomes http://site.com/a/b becomes http://site.com/a becomes http://site.com. It keeps doing this until a match is found. e621 does this more than once because there are cases where the URL is nested by date, like in http://site.com/2007/06/05/image.jpg. Usually this algorithm works very well, provided the artist has an entry in the database.
If he doesn't, then the algorithm is probably going to cut the URL down to just the domain, i.e. http://geocities.co.jp. When this happens, you'll sometimes get every artist hosted on that domain.
Why not just dump all the results if you get more than one? Well, there are a few cases when multiple artists validly map to the same domain. Usually the domain is just being used to host files or something.
Is there an API?
Yes. The artist controller uses the same interface as the rest of e621. See the API documentation for details.