Here's a list of sources:
1) The ORIGINAL MYTHS THEMSELVES
Don't be reluctant to quote from myths directly. Translations of texts are often easily available online, and also on Amazon or a library. Sites like Sacred Texts have a large collection of mythological texts , and often times translations of myths can be found with a simple google search (try googling "Gilgamesh read online" or "[myth x] read online"). Make sure that you are aware that many online translations can be out of date, as the most common reason translations are posted online is their copyright has expired (i.e. they are ~80 years old).
However, do be careful to note when some myths have slightly different versions among the manuscripts available (which is almost always the case -- translating is hard [translating old languages is harder], and there will always be disagreements between translators).
2) Footnotes or summaries in books of mythology
A lot of translations of myths have footnotes or endnotes that explain certain words or events. In addition, a lot of books of myths also have a 1-2 page summary and explanation of the myth before the myth itself.
3) Scholarly articles
Academics often study and write about myths, and their articles are almost always good sources. JStor is a good place to look for academic articles, but if you don't have access to JStor, a simple google search can often turn up scholarly articles. Another good source of free academic articles is academia.edu, a quasi social network that allows academic research to share papers online.
4) Well referenced websites by academics/experts
Sometimes, academics/researchers/dedicated amatures will create well referenced sites about specific myths. Some examples:
Generally, the quality of a website is directly correlated with how many sources the website cites.
5) Academic books about mythology
Many academics will write entire books about specific myths. You can buy or borrow these books from a library and use them to answer questions. If you're lucky, these books can be read for free online.
You can learn a lot from deconstructing the names of gods/places/etc. This answer by Travis Smith of Bexar is a good example of how to use etymology as a source of information.
1) Mythological Encyclopedias
There are often many different versions by many different authors of certain myths. Those versions don't always agree with each other. Unfortunately, many encyclopedias don't acknowledge this, and will confuse "source x described god y as having red hair" with "god y has red hair". Be careful when citing encyclopedias that claim to list "facts" about myths or religions, especially if those encyclopedias don't cite their sources.
Wikipedia can often be wrong, but more importantly using it goes against the goals of Stack Exchange. Sites on the stack exchange network are best when they add new content to the internet. Regurgitating wikipedia doesn't do that, and makes this site useless because people could just bypass the site and search wikipedia itself.
Sometimes a Wikipedia article is well sourced. In this case it is still better to not use wiki as a source. Instead look through those sources and develop an original answer from them. In other words, Wikipedia can be a great place to find sources.
3) Children's versions of myths
Whenever possible, quote from original translations of myths. Children's versions are frequently edited to either simplify complicated plots or de-emphasize inappropriate content.
4) Movies and entertainment media
Many authors, writers, and producers make a good living by creating their own adaptations of popular myths. These are typically not representative of the original myths from centuries and millennia past.
5) Pseudo-science attempts to "prove" that a myth is true
There are small populations that believe certain myths are true. The best example would be Young Earth Creationists and the book of Genesis. Additionally, there are groups that argue that Atlantis was real, that gods like Zeus were aliens, and so on. Without committing a genetic fallacy, be very skeptical of the validity and factuality of any claim made by a source that intends to prove the truth of any myth.