Much like installing a plugin in WordPress, installing a theme is quick and easy.
You can choose a free theme from one of the 4000+ available in the WordPress.org repository, or you can install a premium theme or theme from another source via zip file.
Firstly, from within your WordPress admin area you need to navigate to Appearance->Themes
You'll see a list of the currently installed themes, and one of them will be marked as active - that is your current WordPress theme.
On this page, you'll also see a button at the top left, just to the right of the main sidebar menu - this button is titled "Add New" - go ahead and click on it.
You'll be presented with a list of popular themes to choose from, you can browse through these, filter by features, or the latest or most installed themes, or if you know the name of the theme you'd like to install, search for it in the search box at the top right.
For the purposes of this guide, we're going to install the twentyeleven theme.
Once you've picked your theme from the available list, or found it via search, hover over the thumbnail and you will see the option to install the theme.
Go ahead and click on the "Install" button. Once the theme has finished installing, you will have the option to activate the theme now, or you can leave it installed and activate it later.
If you've purchased or downloaded a theme you would like to use, and have a zip file containing the theme, you can install this from within WordPress' admin area too.
Once again, you'll navigate to the Appearance->Themes and then click on the "Add New" button. This time, instead of choosing a theme from the list, or using the search box, we'll go ahead and click on the "Upload Theme" button.
Click on the "Choose File" button, then browse to your theme zip file, and finally, click on the "Install Now" button.
Again, you'll be given the option to activate the new theme now, or activate it later from your list of installed themes (Appearance->Themes from the main menu).