not sure what os your old pc has but go to this site http://windows.microsoft.com/en-us/windows7/products/fe...
download the correct software for you old os. this will collect all you old files settings .pst's and Customisations.
it will ask you how you would like to transfer them i would suggest a thumb drive.
now take the thumb drive to your new pc and click start > all programs > accessories >system tools > windows easy transfer
suggestion when you save the file to your thumb drive create a folder and put it in that, every now and then if screws up if it is not in a folder and wants to save or restore the files from floppy disks.
Do you mean just the pictures, music, word docs, etc or Windows and everything?
Do you have a home router? If so, you connect both systems and share the old hard drive them copy them over.
If not, you can copy to a portable hard drive then connect to the new PC and copy to there. If you can't afford a portable drive, you can unplug the old drive, plug it into the new system (if the new one has the same connectors), and copy off. OR, you can buy a "USB-to-whatever kind of old drive you have" cable so you don't have to open the new case and risk damaging anything.