The easiest way would be to have the Arduino interpret the data it is being sent, and react accordingly.
For example, you could send "T(Show this on the LCD)", and the Arduino would see that the first character is a T (for text), and show everything between the ( and ) on the LCD.
You could send "P(1, 3)", and the Arduino would see that the first character is a P (for position), and parse the row and column values, and set the cursor correctly.
You could come up with other "commands" for the Arduino (C, for clear, etc.).