Hello. It is one of the easiest things to change or insert a graphics card so don't worry about it.
You need to make sure of course that first of all you are buying the correct interface, that is, if you can you want to have a PCI E card instead of the old type which is called AGP.
I suppose if you have a dual core CPU then you most likely have a motherboard with a PCI E socket already but just thought it was worth mentioning.
Another thing to consider is the power increase on the system. when I got my last graphics card upgrade my PC would not boot unless I disconnected something else. I realised then that my power supply was no longer enough so I got a new one of a higher output and everything was fine.
OK on to the actual installing of the card.
Instead of walking you through it myself, I will just point you to the same thing, already written up by others all over the net.
Here is a great video on youtube that shows you exactly what to do:
This video has a bit of comedy to it but it actually is quite good for pointing out the basics for those who are not adept at going inside their PC tower so have a look at it too..it is a bit dated though and the guys card is an AGP one, your PCI E slot will be smaler than the one in the video.:
This video will give you another look and he talks of PCI E too and shows you everything you need to know. by watching these you can familiarise yourself with it and then you will be raring to go!
These articles will tell you everything you need to know, don't be put off, they are simple, easy to follow and step by step:
Best of luck.
One thing - you do not need to go buy an anti static strap, just, leave the power lead in the back of the PC but switched OFF at the wall socket. Then when you open the tower, touch the side of the metal case inside, or the power supply inside with your hand...that gets the static charge off of you and basically makes the chance of static doing anything very slim. You can now take the power lead out of the back too before carrying on with the process.
I never had an anti static strap and I have changed a lot of components with no static related problems so beware of some articles putting a bit too much weight into the idea of buying an ati static device!
Let me know how it goes won't you..