How to know which RAM I can/should buy for my PC?

If you open the Device Manager (Windows 7 & 8 it's from Control Panel > Device Manager).

Then open the "System Devices" item and it should list all sorts of stuff to do with your motherboard. Mine (for example) has several starting with "Intel(R) 82801" and "Intel(R) G33/G31/P35/P31". These should give you a good start on finding your motherboard model.

As to what memory sticks to buy - go for 2 matched sticks 2 x 2GB as this will allow your motherboard to access it in dual channel mode as this will be quicker.

You might use CPU-z to get memory information. If it fails to read the information then sometimes even the CPU specification is sufficient to know the right memory type. For example Athlon 64 in Socket 754 and 939 uses DDR memory while AM2 uses DDR2 and AM3 usually is combined with DDR3 (but supports DDR2 from the CPU as well, so there are some mainboards providing DDR2 but most have only DDR3 sockets).

You might post CPU-z output here to clarify.

How many memory sockets does your mainboard have? Hoe many modules are already installed? Can you just take out the module which is currently installed and read the model information on it?

Likely you will find some information like "PCxxxx" (DDR) or "PC2xxxx" (DDR2) which makes it easy to find the right module type.

But when you open your PC anyway just have a look at the mainboard. Typically there is some sticker or print on the PCB stating the concrete model so anyone can find detailed information online then.

Regarding the number of modules: Most CPUs since Socket 939 feature Dual-Channel memory access. This means if modules are installed in pairs it can access them in parallel (2x64-bit bus width) and therefore increase the memory bandwith. If you just install one module or install module with different capacity then either dual-channel feature is disabled or it just works for a part of the memory size.

Assuming you currently have just one module (1x1GB) installed I would recommend to get another 1GB module so you have a pair of 1GB modules installed (2GB total). As long as you don't have any specific programs which demand more memory this should be sufficient for Windows 7 and some office use. It does not make much sense to invest a lot in such an old machine. Getting a single 1GB module should be pretty cheap though.