How do I create a gallery page?

You should try to install the NextGEN gallery plugin.
http://wordpress.org/extend/plugins/nextgen-gallery/

With it, you can easily achieve the page you want. Once installed, create a few galleries and upload your pictures. You can order your single galleries into albums. On the pages listing the galleries and the albums, you can see their unique ID.

Look the codes here: http://wordpress.org/extend/plugins/nextgen-gallery/faq/
You can list single galleries, albums, slideshows of a gallery, and a lot more.

Paste the codes on in a page or post in the editor where you want them to appear, changing the gallery/album ID to the one you need.