What might cause the alarm to go off on our 2004 Jeep Grand Cherokee and how do we turn it off as the owner's manual was not helpful?

I tried pressing the red alarm button on the remote, but that didn't work. I
wound up opening the driver's door (I believe with the remote, but I was very
anxious and can't exactly remember), but once inside I tried but failed to
turn the car on thinking that would turn off the alarm, then I started pressing
all the buttons on the drivers door and something there turned the alarm off.  
Our local Jeep dealer said he thought inserting the car key into the driver's
door would do the trick - is that the answer???