Turn the computer off.
Remove the battery.
Unplug the AC adapter.
Turn the computer bottom-up.
Look for a few screws that secure a small panel.
Unscrew those screws, and remove the panel.
If you've selected the right panel, you should see your current RAM.
On the LEFT and RIGHT edges, there are small "fingers" that are holding the RAM.
Gently pull those fingers away from the RAM, and it should pop-up slightly, and you should be able to remove the RAM.
Notice that the "notch" in the middle of the RAM is slightly off-centre.
Insert the new RAM into the socket, and gently press down, until those two fingers "click" to grab the new RAM.

Depending on your "old" RAM, you may have:
* one "occupied" RAM slot (1GB), and one "empty" RAM slot;
* two "occupied" RAM slots (512MB/stick).

So, you may have to remove one RAM stick, to expose an "empty" RAM-slot "hidden" under the RAM.
Or, the "empty" RAM-slot may be visible without removing the RAM.

Or, you may have to remove one of the 512MB RAM-sticks, in order to free-up a slot for the "new" RAM.

Replace the cover-panel, and screw it in.
Reconnect the battery.
Reconnect the power-supply.

Start the computer.
Click Start
Point at My Computer
Right-mouse click on My Computer
Choose Properties
It should display your CPU-speed and the "new" amount of installed RAM.