You should open your blog and sign in.
Then you should click on ‘Appearance’ and hover the cursor to theme’s link. After clicking on the link, you will be shown all themes of WordPress. Explore through the options, you will be given an option to preview how your blog will look like after the selection of a particular theme. Keep checking until you are satisfied and when you find the right theme, save it.
If your blog is not free and you have a separate domain name and host, you would have to contact your ftp client. You can also do that by signing in with your ftp client and choose a theme of your choice. In this case, you will have to download a theme in a zip file and then extract it in a separate folder. After the theme is downloaded, you should upload it to the new theme folder as yourblogname.com/wp-content/themes.
Now open your blog, sign in and go to themes by clicking on ‘Appearance’. Now you will be shown a preview of your downloaded theme, if you like it then save it, otherwise do not activate it. Do the same process again to apply a different theme, and save your desired file.