From any individual overview page or from the tree overview page, run mouse over "tree pages" link and click on "tree settings" in drop-down list.
On the right is option to export your tree.
What method you use for download will depend on what type of desktop genealogy program you have (latest FamilyTreeMaker or other). Follow the prompts.
For most desktop programs you can only export tree as gedcom file. This will lose all photos, stories and most citation-links to ancestry.com sites.
You can not download another person's Ancestry Member Tree, although some of the trees on Rootsweb's WorldConnect allow downloading a gedcom file.