How to read the IPA vowel chart

The IPA vowel chart looks weird and abstract. What is this quadrilateral? How the heck do you read this mess? Am I supposed to be able to tell how to say each vowel from its position in the chart?

Fortunately, yes, the position does tell you something. It tells you the tongue position.

When you speak a vowel, your tongue makes an arch. The arch's apex position determines the vowel that comes out when you speak. (See here.) The tongue's apex position varies along two axes: Top to bottom and back to front. These correspond to the two axes in the IPA's vowel system. The IPA vowel system classifies tongue positions into discrete "coordinates" along each axis:

1. Top to bottom. Falls on a seven-point scale from close (at the top of the mouth) to near-close to close-mid to mid to open-mid to near-open to open at the bottom.
2. Back to front. Falls on a three-point scale from back (back of the mouth) to central to front (near the teeth).

In the IPA vowel chart, the top represents, intuitively enough, the top of the mouth, while the right side of the chart represents the back of the mouth.

Here's a simple example of how to interpret these terms. [u] is called the close back rounded vowel. Breaking down the words in the vowel's name:

1. "Closed" means the apex of the tongue is close to the top of the mouth. That's the top-to-bottom location.
2. "Back" means the apex of the tongue is in the back of the mouth. That's the back-to-front location.
3. "Rounded" means you close the corners of your lips so the opening between your lips makes a rough o-shape.

To speak this [u] vowel, you want the apex of your tongue near the top of your mouth in the back, and you want to round your lips by closing the corners of your lips together.

The closest analog in English, apparently, is "boot." It's not quite the same sound. It's "more front" than the "pure" vowel would be, hence the plus sign underneath. It's also a long vowel, hence the colon. But it's pretty close. If you can say "boot," then working backwards, you can try curving your tongue back a little so the apex is closer to the back of the mouth. That should give a sound closer to the "cardinal" [u].

So, to speak a vowel from the chart given its position (top-to-bottom, front-to-back), you arch your tongue so the apex is in the appropriate position and speak.