In questions such as this one (What’s the pronunciation for loathed) answerers often answer pronunciation questions with special characters, as Matt does for that question by using ləʊðd. Though I already know how to pronounce the word loathed, I for the life of me can't look at those special characters and figure out how the pronunciation comes from them! How exactly do they work? Is there a reference somewhere for how each character is to be pronounced, so I can get a better handle on this system? It makes it hard for me to read questions and answers containing these symbols when I don't understand them.
The characters are from the International Phonetic Alphabet or IPA. To cover it fully would take more space that we've reasonably got here, but the Wikipedia link above should help you out if you care to dig in. Also, here is a link to the offical chart of the symbology.
And one more: this Merriam Webster pronunciation guide might be a better place for a first look.
If you don't expect to extend your use of the IPA beyond English, or if you'd like an easy way into it, the Wells Lexical Sets are a very helpful supplement. Here’s a ‘remapping’ I contrived for my own easy reference; where two IPA symbols appear opposite a keyword, the first is RP (Received Pronunciation) in British English, the second is GA (General American):
I am super late to the party here, but I myself learned IPA in college only because I was interested in learning phonology in general and it's not possible to have a conversation about phonology without knowing some phonetics. Put differently, I don't think I could have learned it (or at the least I would have been extremely bored) if I had had to memorize the symbols without any context.
Ten years later, it has been extremely helpful as I have unexpectedly had to learn French. It gives me a lot of sympathy for English learners, because, as in English, the written form is very old and does not represent the spoken form well.
I recommend the investment of time for anyone who is interested in learning to pronounce a foreign language or to teach pronunciation of English, but I don't recommend trying to memorize symbols right away. Instead, learn about the difference between a phoneme and an allophone of the same phoneme within a language (this is really interesting, by the way-- feel where your tongue is in your mouth when you say the first letter in "cop" vs. "keep" for instance -- in Arabic, those two places are considered different sounds). Then learn about place and manner of articulation of consonants. Do vowels last, they're the hardest and most boring :-)