The eMachines ET1331G desktop computer uses the eMachines NexGen 3 computer case.
Looking at the computer from the Front, the Left Side Panel removes.
Looking at the back you will be viewing the Right side.
There are two screws to remove, then the side panel is slid Back. (Towards the rear of the computer)
There is a raised protrusion in the middle of the Side Cover on the back. This is where your fingers go to pull back on the Side Panel.
There is one screw coming down from the top, on the edge of the Side Panel, and one screw coming up from the bottom.
(Philips head screws)
Slide the Side Panel back. It will only slide back so far, as there are tabs coming from the Side panel, into slots of the computer case.
Once it stops sliding back, take it straight out to the side. Lay the Side Panel aside.
Here is a photo detailing the back of the ET1331G from eMachines Support,http://support.gateway.com/emachines/desktop/2009/emachines/et/ET1831/ET1831rv.shtml
The two screws on the Right side, as you are viewing the computer from the Rear, as shown here.
1) Computer UNPLUGGED from power
2) Observe Anti-Static Precautions BEFORE reaching inside the computer, and BEFORE handling hardware parts.
Your body carries Static electricity.
Static WILL fry out (Short Circuit) the hardware components in a computer.
Computer on a table, computer unplugged from power, computer case open.
TOUCH the metal frame of the open computer case to relieve your body of Static.
Should you leave your computer in the middle of working on it, be SURE to touch the metal frame again upon your return.
For additional questions please state in a Comment.