How can I have multiple languages in my iPhone dictionary? I speak English with most people but correspond with my mother in Spanish.  

Is there any way I can get autocomplete on my iPhone to work for words in both languages?
Yes, add another keyboard to you iPhone.  I did it with Russian, follow this website, pretty easy.

Activating the keyboards is straight forward. Tap the “Settings” icon and then select “General”. Then scroll down and select “Keyboard” and then “International Keyboards”. There you will see the long list of languages available — simply flicking the toggle to “ON” will activate the keyboard. You can activate as many as you like.
Now that more than one language keyboard has been activated you will see a small globe key on all keyboards. Simply tap the globe key to toggle between all the installed keyboards. Simple, elegant and clever.