Once all of the photos are downloaded to the computer, the computer might give you the option of deleting the photos from the camera's memory card or viewing them. I would recommend not deleting the photos from the memory card until you've had a chance to make a backup copy of the newly downloaded photos.
Look through the photos -- while it's still fresh in your mind where you shot them and what you are trying to accomplish with the photos -- and delete any poor ones. Taking a little extra time now will save you time in the long run.
Most of the time, the camera gives automatic, generic names to the photos, such as "Sept 10 423." It's always a good idea to give the photos a name that will be easier for you to recognize as you're looking through them later.
Finally, if you simply cannot make the connection between the camera and the computer -- even after you've consulted your camera's user guide for instructions specific to your camera -- you have the option of taking the memory card to a photo processing center, which should be able to copy the photos onto a CD. You then can download the photos from the CD to your computer.