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.