If you are content with remaining at wordpress.com where you can only use these themes and no others http://wordpress.com/themes/ then you can change themes as often as you wish to.
If you want to change themes on a free hosted WordPress.com blog you must be logged in under the exact same username that registered the blog and who is the Admin of the blog. Note that no content is ever lost when changing themes.
Go to Dashboard > Appearance > Themes
browse themes until you find one you like and click "activate"
or type in the name of the theme you want to use and
click the "activate" link when it appears
After you change your theme all you need to do is go here Dashboard > Appearance > Widgets > Inactive Widgets and re-install them where you want them to appear. The widget contents and settings will be the same as they were prior to changing themes.