Finding a New Theme

There are dozens of websites where people make free WordPress themes available. No matter what the subject matter or topic of your site is, it is likely that you will be to find a theme that comes very close to matching what you want.
Try searching Google using a search term like 'free WP themes' or just 'WP themes' to see what you can find or try to shortcut the process of finding something you really like by searching for 'your topic + theme'. Alternatively, try searching any of these sites to see what there is that is appropriate to your topic or subject matter:
http://wordpress.org/extend/themes/
http://topwpthemes.com/
http://www.wptmp.com/
http://www.freewpthemes.net/
http://www.wpthemes360.com/
http://www.elegantwpthemes.com/
http://wptheme.net
http://wpthemeland.com
Many of these sites are searchable, so you should be able to find something that matches your requirements fairly easily. This would work for my dog related site, although the puppy pictured is not a boxer as I would prefer it to be (but is often possible to change the header graphics fairly easily in any case, so this will be fine to start with):

I would click the 'Download' link to grab this particular theme. When you download it, the theme will be zipped, so you need to unzip it once it is on your machine.
The next job is to upload it to my site, which necessitate using an FTP program.