You need to purchase Two sticks of 1GB DDR2 RAM.
If this sounds like cryptics to you.http://www.newegg.com/Product/Product.aspx?Item=N82E16820231116
You will be able to unscrew the back of you laptop, and see the current Memory Chips in there, remove them and replace them with the new memory sticks.
This isn't your exact laptop model, but the procedure will be the exact same. The chips will just be in a slightly different location. You may have to unscrew a different looking compartment on the back.http://www.youtube.com/watch?v=sTm4AhdrCCE
Here is the user manual with official written instructions.http://esupport.sony.com/US/p/model-home.pl?mdl=VGNNR110E&LOC=3&session_id=3f88e8baed8f06f51989878d8f7edc99#/manualsTab
The PDF of the User Guide is the one you want, it has a section called Adding and Removing Memory.