How does the iPad auto-correct work exactly?

Solution 1:

AutoCorrect will automatically replace the word unless you cancel it manually by tapping it. (Note the small × sign in the suggestion bubble indicating that tapping it will cancel the suggestion.)

So, as soon as an AutoCorrect suggestion appears that you want to use, just hit Space (or insert a punctuation mark) and continue typing.

Solution 2:

If you are typing and your iPad suggest you something, you should just continue typing or hit the spacebar and your iPad will correct it automatically.

If you take a close look at the suggestions, you'll see a small cross at the right side. Clicking on the suggesting, will make the suggestion disappear since you closed the pop-up.

And once you've closed the popup, it won't be shown in the same word again if you retype the same word.