How to serially communicate arduino uno to PIC18f4550?
yeah you can quite easily do the Serial communication between Arduino and PIC Microcontroller. You need to connect the below pins:


Arduino TX will be connected to PIC RX.
Arduino RX will be connected to PIC TX.
GND of Arduino must be connected to GND of PIC.


Next thing you need to remember is to have same baud rate for both Arduino and PIC. Now you should check these two posts:


Arduino Serial Communication.
PIC Serial Communication


First one is explaining the Serial Communication of Arduino while the second one is Serial Communication of PIC Microcontroller. You should also read What is Serial Port? to get more idea about Serial communication.

I hope they will help you out. If you still got into some issues then let me know.