Personally I find Picasa the most user friendly software to use.
When you download from your camera, you need to decide how you store your photos on disk. You could have a folder for each year or month. Often the default is that the cameras utility software creates a new folder each time the camera is downloaded but you can change this.
When Picasa is installed and run for the first time, you have to select the folders which are to be added to Picassa. You cannot just browse folders as when using Windows Explorer. Once you have added folders, you can set which folders are continuously monitored by Picasa for new image/photo additions.
Try to store your photos in at least three places. i.e. original + 2 backups in case the original and primary backup fails (it does happen!). This could be done simply by archiving your photos to another computer and a DVD every year or sooner. You could also upload your photos to the "Cloud". Google, Microsoft, Flickr and others provide free space, 2 GB seems to be the most space available free (I think come companies offer 5GB free, I can't remember who though)