Technical FAQ:
Sequencing and timing

• I display images in sequence but I see only the last one. Why?
• How do I display a message for a few seconds?

Oh, the second article of the FAQ should be read first, too...

Some problems with your code:
- As said in the articles, avoid using delay(). Eg. if you want to do an animation somewhere (like an animated background), it would ruin the effect.
- The size() in a loop is unexpected and totally to avoid. It should always be the first line of setup() (or of your code, if that's all of it), and that's all.
background() is enough to clear the sketch area.
- chatAt() returns a char, not a Character. Java automatically converts between these types (auto-boxing / -unboxing), but it is a useless, costly conversion.

Spoiler of the above articles: use draw() as the loop, so create a global counter (with a name longer than 'i') to keep track of the currently added character.
You will need to use str.substring() instead of charAt(), otherwise you will display only one char at a time.

As an exercise for you, I prefer not to display the solution... Try to follow the advices, and if you are still stuck, show your progress and we will guide you further.