Plenty of tricks exist for learning new alphabets: flashcards, visual and sound association, transliteration, drawing letters, and so on.
These can all work great, but I confess my method of learning new letters is largely brute force. It’s not a barrel of laughs, but it works for me. I thought I’d share it because it might work for you better than all the association tricks.
By alphabet, I mean writing systems in which each sound has roughly one symbol to represent it. In other words, I’m counting Hebrew and Arabic, even though they’re abjads, and Japanese Kana, even though they’re syllabic. I’m not counting Chinese characters/kanji, which I don’t know any way.
Sounds First
I’m big on input. I’ve only once tried to learn an alphabet without first getting a fair amount of audio input in the language. In every other case, I’ve spent at least a week listening to music or news broadcasts (Thank you, Radio Free Europe) for an hour or two a day. This way when I read a written explanation of a sound, I already have an idea of what it really sounds like.
Thing is if you try to guess a letter’s sound based on a written description, chances are high that you’ll get it wrong. That incorrect sound will then stay stuck in your mind and cause you to mispronounce words. Lots of listening also helps prevents you from developing incorrect intonation habits from your slow reading.
You don’t have to recognize every single sound before you look at the written alphabet—especially if the language has a lot of sounds that seem similar to your ear—but the more you know the better.
Meaningful Transliterations
After some listening, I get a list of my target language’s letters and their English equivalents. Try to avoid using equivalents in another language—for example, Greek into Russian when you’re a native English speaker—or you’ll end up with a double accent. No, really. You will. It may not cause permanent damage, but it will be annoying. (Then again, Rusbrew was actually kinda fun.)
This list should come along with explanations of the differences between your new language’s sounds and your native language’s sounds. It should tell you, preferably with drawings of lip and tongue placement, exactly how to pronounce each sound for which there’s no equivalent in your language.
In any case, for me the equivalents in English are just rough guidelines to jog the memory. I want to match the letters to the sounds I’ve already heard in that language, not to English approximations. I’ll look over the list to see if any letter stands out as particularly memorable, but don’t spend much time trying to “memorize” each letter.
Jumping Right in
With the list handy, I’ll grab a text in the new alphabet and start reading…one letter at a time. Know the first letter? Nope. Look at the list, find the letter, check what sound it represents. Know the second letter? No again. Look at the list, find the letter, and so on. When I get to the end of the word, I read it again hopefully without stopping to look up any letter. See what I mean by brute force?
I’ll keep doing this for three or four days, about half an hour each session, or until I notice certain letters are giving me trouble. When I notice I keep confusing one letter with another, then I turn to mnemonics to keep them straight. More specifically, I make up a mnemonic to contrast the two or more letters I keep mixing up.
As an auditory learner, my favorite is sound association. So if I wanted to remember the Arabic letter gim*?, (a curved line opening on the right with a dot inside the curve) makes a sound like j (unless you’re Egyptian, etc.), I might remember the letter looks like a cover with a precious “gem” inside.
I wait so long to use any memory aids because I don’t see any sense wasting time inventing mnemonics for letters I can easily remember. I prefer to grab a list and start reading so I’m increasing my reading speed and getting more input instead of just memorizing shapes.
Like I say, it’s not the most entertaining method and it takes tenacity, but I find it to be the fastest for me. I’ve worked out this system on Cyrillic and Hebrew, then used it for Georgian, Armenian, and Arabic. But I can’t read fluently in all those alphabets. It’s hard to read fast when you don’t understand a blessed thing you’re reading. 
Have any tricks for learning alphabets faster? If so, leave a comment to help out other FFLL readers.
*Sorry, still trying to get Wordpress to let me use different alphabets.
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I found the Thai alphabet particularly difficult to learn because it has many elements.
If you are going for broke, you need to know the initial sound, the name taught to Thai school children, whether or not it changes if it’s at the end of a word or if it never appears at the end of a word at all, and the class as well (high, medium, low).
I bought flash cards. I used YouTube videos. I taped an alphabet poster to the wall (then later, I used that same wall to bang my head).
I didn’t learn the Thai alphabet until I came across a simple product using mnemonics/associations. The graphics are not pretty, but I quickly learned the shapes of each letter, the beginning and ending sounds, and their class.
Using the same product I also learned Thai numbers in about ten minutes.
The kinder Thai names I tackled at a later time.