You don't tell us which motherboard you are using, but most modern (desktop) motherboards support dual channel memory. Dual channel memory requires two DIMMs to work. Most motherboards will run with one DIMM, but they will run somewhat slower, because they have to access the DIMM twice in a row to get what they would normally get in one shot (from two DIMMs). If you only want 4GB, you are better off with 2 x 2GB instead of 1 x 4GB, so that you get dual channel. Adding a second 4GB DIMM is a good idea, but it must be the same size / make / model / spec as the current DIMM. Also, make sure you put it in the right slot. Generally, the motherboard will have two different colours of DIMM slots. Put the second DIMM into the slot of the same colour as the current DIMM (that will set up dual channel for you). It is common for the two slots of one colour to be interleaved with two slots of another colour.
Laptops are different from desktops. They will run happily with a single SODIMM.
Using 2GB of RAM without any programs running is unusual. I'd be somewhat concerned about that, because it could mean you have malware of some kind running. You might want to check to find what it running, and how much RAM it is using. Task manager will show you what is going on if you add a few columns to the Process display.
I would also suggest scanning your machine with legitimate anti-virus / anti-spyware / anti-malware software. Be careful not to fall for any fake AV - there are some quite sophisticated ones. Buy some real AV software (Norton, for example). If you don't want to pay, then use something like Microsoft Security Essentials.