Pretty much the same like
that one. The difference: Instead of moving the text-layer, you'll put an opaque layer (with a coloured box on it) above it which hides all the text. you would move the opaque layer to the right, making it reveal the text after a while.
A quick example:
for the "true" typewritter effect, with a letter after the other, you could do frames for every letter and add a letter at a time. this can soon get boring for longer texts, as it is a lot of work for you. on the other hand, you could even vary the times between the appearance of the letters, so it would give an more organic feel.
try playing around with the Animation Palette of ImageReady and tell us how far you got :-)