Hi
Start by checking what EMachines sat is the maximum RAM and RAM Clockspeed the motherboard can support (as it's an XP machine, I suspect it may be 2Gb max). Then make sure you buy 1 stck of the correct RAM (there seems to only be 1 RAM slot).
Disconnect from mains power.
LCD Monitors, TVs and All-in-One PCs have a dangerous internal working environment, containing several Capacitors that store a gigh charge capable of seriously injuring or even killing an inexperienced repairer.
If, for economic or educational purposes, you are determined to do the repair this yourself, you need a large sheet of paper on which to sketch a screw location diagram of the rear of the LCD Panel.
The first step is to remove the rear cover pf the LCD Panel, often the stand will also have to be removed as well. This is almost always not straightforward. (see review on:
http://reviews.cnet.com/desktops/emachines-ez1601-01/4505-3118_7-33721162.html)
Use the diagram to intelligently map the locations of the different types an sizes of srew you come accross while opening the rear cover.
Be very careful to remove every retaining screw before trying to lift the cover off (there are often several hidden srews and it is easy to miss one and snap off part of the cover or the frame it connects to). Do not use force - if the cover will not lift off easily, look for more retaining screws.
Once the cover is off, you are looking for laptop type RAM Memory Modules, with parrallel side clips that, when pulled outwards with the fingernails of both thumbs allow each Memoey Module to spring up at an angle, enabling to slide it out of its socket.
To replace the memory slide each new module in the correct orientation (there is a notch that only permits the corect orientation) until it is fully docked in the socket. Then press down until the two side clips catch and lock into place.
Now place the cover open face up on a desk or table and carefully place the LCD panel onto the cover, before connecting, powering up and testing the computer with its new RAM, before reassembling it.
Hope this helps.