While joining forces is a great idea to make a community more successful, using the term 'merging' is incorrect. There is not just one button Wikia can push to make two communities suddenly become one community. This is both due to the technical limitations of MediaWiki software, the unique way Wikia user tables are configured, and the fact that two wikis may have pages with the same name but different content (for the technically-minded, a "collision").
There are more limitations to consider, such as viability and community harmony. Please read this Wikia policy page for more information on whether or not a community merging is a good idea.
However, Wikia can offer a different version of "merging", the steps of which are documented below. Note that the word 'merger' is used very differently on Wikipedia and do not apply to wikis.
When to merge
Merging active communities
The best reason to merge is when the active communities on multiple wikis realize that their work would be more organized and attract a larger number of readers and contributors if they were combined. In this case, the admins and users of the wikis should discuss the merger thoroughly, making sure to advertise the discussions on both wikis so everyone involved has a chance to contribute ideas.
When there is a consensus that the merger should go through, users can begin merging the content as described below, or contact Wikia staff for technical assistance. Provide a link to the merger discussion to staff; otherwise they'll need to ask for clarification that the merger is a community decision, not one user's whim.
Merging inactive communities
If the topic is of general public interest, Wikia staff generally prefers to leave dormant wikis available for adoption by new users; inactive wikis do no harm to active projects, and the resources required to host and protect the wiki from spam are manageable.
However, the most probable reason why a Wikia becomes inactive is because it relates to a very specialised topic that attracts too few people; in these cases it sometimes makes sense to merge the content and redirect the url to a more general active wikia that shares the topic.
Research and approach
First find out if the wiki is new; if it has only had a month or two to grow and attract contributors, Wikia is unlikely to be willing to merge right away.
Then, check whether or not there are still active editors. Visit Special:RecentChanges on the wiki, and use the "in last 1 | 3 | 7 | 14 | 30 days" links to look farther back in the wiki's editing history. Check Special:ListUsers on the wiki to find the most recent editors and/or admins; on small wikis the founder will usually be the only one with both bureaucrat and sysop rights. Try to contact the founder, using their talk page and/or Special:EmailUser.
If there are active Wikians, approach them politely about merging. Offer a friendly invitation to edit at the more active wiki, and let them know that it's possible to move articles and merge the projects so that everyone will have greater success. Always be kind about a community's work -- telling people their project is inferior or pointless won't convince them to join you, it's more likely to drive them away from Wikia altogether.
How to merge
If the merge has been discussed at both wikis and agreed upon or there have not been any active editors for a couple of months, and the admins are agreeable or unresponsive, you may start merging content. As all Wikias share the same account data, if there are a small number of articles, transferring content can be done manually and does not take too much time.
You can move any articles from the site that was not selected to be the wiki URL to the site that was using the following method.
Use Special:Export page on the wiki that will be closed and redirected to create XML pages with author and page history
Use Special:Import page on the wiki being kept to import the XML (requires admin rights)
See Help:Export for step-by-step instructions on the process.
If there are many articles, or if you need additional technical help (such as importing into a different namespace), please contact staff first.
Inform Wikia staff that a wiki can be shut down. You can do this by leaving a message at Special:Contact, which should include the following information:
a request to merge
confirmation that there is community agreement for the merger, with links to any on-wiki discussions, OR confirmation that there are no active editors and that you've tried to contact the founder
links to both the old and new Wiki making clear which is to be closed
confirmation that all of the content has been transferred from the merging Wiki into the merged one
A staff member can then close down the inactive wiki and redirect its domain name to the new destination. The communities will now be under one Site Name and URL.
(Any redirected domain name can become the primary URL for the merged wikis, if the community chooses.)