Arduino-Arduino over Serial

Hi,

I'm pretty sure I've got this right, but to connect two Arduinos over serial, I just connect the TX on Arduino1 to the RX on Arduino2 and vice-versa?

The reason I ask is that I'm also not sure how to troubleshoot this situation. I want to avoid connecting the boards the my computer when they're trying to talk to each other, right? So how do I go about figuring out why it doesn't work without connecting to my serial monitor?

Maybe this is obvious. I'm exhausted. Please let me know what you think.

I think you also have to connect the grounds of the 2 Arduinos togehther.