How do I connect multiple shields to my arduino and have them all function?
The ethernet shield is SPI. A quick look at the schematic for the LCD shows that the pins it uses don't conflict with the SPI ethernet pins, except that pin 4 is used as the SS pin for the SD card on the ethernet shield. You have to deal with this. You might be able to cut the track on the LCD shield to pin 4 and wire it to another pin. You'd also have to change the LCD software.

The LCD shield uses analog pin 1 for the buttons, so pick other analog pins for the accelerometer.

Adafruit.com have an LCD 'backback' that allows you to drive those 16x2 displays from I2C or SPI, which reduces pin conflicts.

This is good shield resource http://shieldlist.org/ and it lists the pins for each shield.