OVERVIEW

In order to avoid legal troubles and satisfy the moral obligation to compensate creators for their work, you MUST own a copy of a film (or show) both if you intend to create your own fanedit AND if you intend to view someone else's fanedit.

WHAT CAN A FANEDIT BE?

A fanedit can look like almost anything. It could be a rescore: a total reconstruction of a film's soundtrack; it could trim scenes for better pacing; it could re-introduce deleted scenes into the film; it could take all these things together and fundamentally alter the film's story.

Perhaps the two Ur-examples are the Star Wars Prequels and Warner Bros. et al.'s The Hobbit Trilogy.
Many fanedits exist to remove elements from the Star Wars Prequels (such as the entire character of Jar Jar Binks) or overall tighten the pacing and narrative flow. Rogue Wave Observer recommends HAL9000's Prequel Trilogy for those interested in either a Star Wars Prequel fanedit or just generally in what a fanedit can be.

After the release of The Battle of the Five Armies, many, many fans took to their editing software and sought to drastically trim down the Hobbit films. Some fans just sought to trim the runtime and remove gratuitous CGI or comedy scenes, while others desired to adhere more strictly to J.R.R. Tolkein's book. As of Stardate 23070.8, Roge Wave Observer recommends The Cardinal Cut, although there are some framerate stutters on occasion as an artefact of the film's atypical filming framerate in conjunction with how the editor exported the video. These are only noticeable on the sweeping landscape shots, and likely only to weirdos who care about such things.

LOCATING FANEDITS

Obtaining fanedits can be challenging. It is not uncommon to find websites that list fanedits but do not have links to any (such as the IFDB). Even some site that are bold enough to have links may not have any meaningful information about the linked edits (such as The Fanedit Network). Generally, distributing links is obfuscated or otherwise kept off the beaten path to avoid any possible legal trouble around distributing copyrightted material.

Visit this page for an explanation of resources linked from Rogue Wave Observer.

ARE FANEDITS LEGAL?

This question has no real answer because no law has addressed fanediting as a practice. It would seem to be a safe bet that such copyright holders as Warner Bros., Paramount, and Disney would not appreciate individuals freely offering copies of their owned works, regardless of how modified.
The better question would be, "Are fanedits moral?" Rogue Wave Observer holds that, yes, if you own a copy of a film, you can do whatever you want to with it, including edit it to your liking. You could even recreate someone else's edit of the film yourself, but we share edits to make things easier and more accessible, which is why you MUST own a copy to view an edit.

HOW CAN I FIND A FANEDIT?

The most surefire way to find a fanedit is to find someone who has a copy of it.
Some sites exist where links are provided. The Fanedit Network is a website consisting exclusively of links to fanedits; as mentioned previously, it does not contain any information on the nature of these edits. Posts on r/fanedits often include links to Google Drive or Mega Drive; sometimes these will be encoded in Base 64.
The Fanedit Central Databse has a gargantuan list of fanedits with nearly all including a link to a forum post, and some with download links.

The other method, arguably a more specific version of "find someone who has the edit" is to reach out to the editor directly.
Two large hubs for fanediting are the OriginalTrilogy forum and the IFDB forums. Neither site has public links (OT has a more involved process to view the forums), but if you have the name of the editor, you can track them down on a forum and send a direct message requesting a download link. This is considered the ideal method by the IFDB (be prepared to prove you own a copy of the original film).