your handycam should have come with a software cd. This has a program which enables you to transfer your movies to your hard drive. The connection is usually via usb2 or firewire. If you dont have a firewire connection you can easily add one from a pc shop. If its usb, then you will no doubt have a free port on the pc.
You have to convert avi/mpeg to dvd format before you can burn them to onto dvd media. If the sony didnt come with a program to convert, I suggest winavi as it's very easy to use and very fast. To burn to dvd after converting, I suggest nero express, its so easy to use.