How do I get my digital photos into my computer?
Your digital camera should come with a cord that connects to your camera at one end, and has a USB connection at the other end (the larger connector). With the camera on, connect the cord to both devices. There should be symbols on the cord and on the various ports on your computer that you can match up. Computers generally have several USB ports on them, so find one that is free. Some cameras even have a saddle that allows you to put your camera in and the files automatically transfer.

Some computers even have slots to fit your camera's memory card and you can also buy a USB transfer device that holds your memory card and plug into the USB port of your computer. You can then transfer it like any other file on your computer.

Where do I put my photos on my computer?
Once connected, the computer should recognize the camera and open a photo-organization application, such as Windows Photo Gallery or iPhoto. Use this application to import, edit, and rename your photos.
Make a note where your computer stores the photos.
In Windows look for the "My Pictures" folder.
On the Mac look for the iPhoto library inside the Pictures folder.
Once in these folders, you can create subfolders so you can find what you need quickly even if the application that reads them somehow stops working.

What if I want to get fancy?   
Generally the photo cataloging software that came with your computer is fine. If you need something more powerful or want some special effect or photo retouching software there is plenty to choose from. Freeware to powerful professional grade programs are available in Apple, Microsoft, even Linux operating systems.