I use realbasic talking to arduino in a couple of products (for example http://www.interactiondesign-lab.com/idshop/product_rfidmonamour.html
I should extract some code and paste it on the playground but it will take me ages... in the meantime use the example called "serial_read_basic" that you find in arduino already.
Whenever you send an H it will turn on the LED... you can use this as a strarting point.
one the realbasic side you could use code like this (this is very rough now)
given that you have an object called serial1 on your window
If Serial1.Open then
MsgBox "The serial port could not be opened."
this code opens the communication port and talks to arduino.
sending an H
check the help in realbasic and you'll find all the info you need
be ready to write an article for the playground about your experiments