There are several solutions. One simple one is to use google's Picasa program. This will index all your images. You can then export them as a gallery in html all ready to be uploaded to your web site. No need to touch any other program.
Another alternative is to use one of the many gallery scripts. For example Coppermine Gallery or gallery.sourceforge.net are just two. Look on hotscripts.com for more examples. With these you upload the gallery script to your web site. Run the installer. Then you can upload images to your gallery via your web browser. You can also ftp up the images then run a batch run on them. I have used the gallery.sourceforge.net script on a site containing over 10,000 images without any problems. Oh, and you don't have to deal with any html or stuff either. Just follow the install instructions. Your web host might even have an system such as fantastico built into thier control panel that will install several gallery scripts with just two clicks of the mouse.