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Memorizing IPA consonants is trivially easy; each symbol represents one sound, and that sound can be described with a variety of parameters about manner of articulation, etc.
The IPA vowels, however, are a whole other beast. How can they be memorized if describing them is not so easy? Of course, some symbols are just English vowels, which makes them pretty self-explanatory, but other ones like the back medium vowels are a bit trickier. Is there any method to the madness?
If you memorize them while learning to pronounce them you're aided by muscle-memory. They are defined after how they are pronounced after all. The vowels are hard to explain but a tutor can show how to do them. That's how they've traditionally been taught, from mentor to student.
Take [ɑ]: relax the lips, open the mouth just about as far as it goes, try to press the tongue down, do not let the jaw move forwards, vocalize. A mentor can tell you when your mouth is in the right position. Once you've hit the right spot enough times, you've reprogrammed your hardware, and might be moving the mouth into position even when reading or thinking about IPA, which is fine :)
First off, one should keep in mind IPA symbols have no connection to one's native language. For example, i in transcription has nothing to do with i in with. Fortunately, their appearance often suggests the closest sound. For example, ɘ and ɜ resemble a certain similarity to e, but it's not a rule.
So the best suggestion is to think they are pictograms that should be studied individually.
If one prefers more scientific approach, there are three basic characteristics of a vowel:
They form a well-known trapezoid, and it may be a good exercise to try reproducing them with gradual transitions along each axis.
There are more characteristics like length, nasalization, pitch, etc. They are represented with special symbols.
These mnemonic devices can help to memorize the inventory of English vowel sounds. From top to bottom the front vowels can be remembered with the phrase: m(ea)n w(o)men m(a)ke m(e)n m(a)d. And the back vowels with: L(u)ke t(oo)k n(o) (awe) in m(o)ps. Plus there is the lax central vowel.
