Upgrading processors is possible, but you have to do some research. Not all processors are alike. There are two main brands of processors, ones made by Intel and ones made by AMD. Each of these two brands use a variety of different kinds of processors, some of which are compatible and some of which are not.
The first thing you need to do is find out what type of motherboard you have. If you need some help figuring that out, download and run Everest (it's free). This program will tell you more about your system than you knew existed. Look for the information about your motherboard.
Once you have found the information for your motherboard, post it here. Please be as detailed as possible, including: manufacturer, model, and version number. Also include the details of the current processor: manufacturer, model, socket, speed, etc.
If you are unable to find this information, and your system is from a major manufacturer, post the manufacturer and system model number (for example: Sony PCG-NVR23). From that information, we can look up the details of your system. It is still best to use Everest however since that will tell us more about your unique system than a model number will.
Once we have this information, we can tell you if there are processors that are compatible with your system that are worth upgrading to or not.
Most likely, you have an AMD Athlon 64 4000+ San Diego chip currently. This chip has a socket 939 design, so I know that your motherboard supports socket 939 chips, but this doesn't mean that the board supports all socket 939 chips. The X2, dual core, chips have socket 939 designs as well, but I really need to know what specific motherboard you are using in order to reasonably assure you that you can upgrade to a X2 chip. Remember, the upgrade potential isn't based upon what you are upgrading; rather, it is based upon what you are upgrading plugs into and what its capabilities are.
CPU Type - AMD Athlon 64, 2418 MHz (12x202) 4000+
CPU Ailias - San Diego S939
CPU Stepping - SH-E4
Instruction Set - x86, x86-64, MMX, 3DNow!, SSE, SSE2, SSE3
Min / Max CPU Multiplier - 4x / 12x
L1 COde and Data Cache 64 KP
L2 Cache - 1 MB
The board only supports one processor. The dual-core chips is one chip with two cores inside of it, so you would buy an AMD Athlon 64 X2 chip, such as the AMD Athlon 64 X2 4200+ Manchester.
I recommend that you buy a retail package and not an OEM. The retail package comes with a new heatsink and fan. When you are ready to install the new chip, take off the current heatsink, remove the chip (I can tell you how to do this if you don't know), pop the new chip in, and carefully mount the new heatsink.