Upgradation to 1gbram to 2gbram for sony viao VGN-NR110E

well you buy the ram. Then take off some screws on the bottom of the laptop. and then replace the old ram with the new ram. plenty of videos online if you are unsure how to do it.

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=N82E168...
That.

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=VGNNR11...
The PDF of the User Guide is the one you want, it has a section called Adding and Removing Memory.

www.sony.com
- Order more RAM, they will install it.