How to install and change phpBB3 styles
First, you have to download the style to your local computer. The official phpBB site has many different styles that you can choose from.
After you download the style you have to unpack the archive and upload the whole folder to the styles folder in the phpBB3 directory on your hosting account. You can upload the unzipped folder using an FTP client.
Once the unzipped folder is uploaded to the styles folder on your account you have to install the new style. You can do this from the administration control panel of your phpBB3 forum. After you log in to the admin panel click on the Styles tab and then click on the Install button that's right next to the name of the new style. When you click on the Install button you'll see a couple of options that you can configure. If you leave them as they are, the style will be active but it will not be your default style.
To deactivate or make a style the default one click on the Details button for the particular style on the Styles page of the admin panel and configure the necessary settings.
Keep in mind that registered users can choose their own style from the ones you have activated. You can, however, force the default style on all users. To do this click on the General tab of the admin panel, then click on the Board settings link on the left, and from the options that appear mark the Yes button for the option labeled Override user style. From the Board settings page you can also change the default style.
If the default style is not forced on all users, it will be used by unregistered (guest) users, while registered users can choose their own default style. To change the default style only for anonymous users click on the Users and Groups tab of the admin panel, then click on the Manage users link on the left, mark the checkbox labeled Select anonymous users and click on the Submit button. Then from the drop-down menu in the upper right corner select Preferences, and from the options that appear set the drop-down menu My board style to the desired style and click on the Submit button to save the changes.
For some more details and screenshots check out the phpBB3 Styles Tutorial.