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Installing WordPress Themes
OK - so now you're ready to install the theme
you've chosenBefore you do that, though, it may be helpful to make sure your folders are organised effectively.
How you do so is entirely up to you, but I arrange mine so that the folders on my server and the folders on my PC are absolutely in sync.
I find this makes it easier to make sure I upload the right files to the right places!
You have two options for installing themes: you can upload them manually or install them through the WordPress admin screens.
Manually Uploading and Activating a Theme
So, assuming you’ve got your folders well organised, download your new theme to your PC. It will be in a zip file. In this example I've downloaded the lgr-royal-red-10 theme.
Step 1: Unzip the files into the wp-content/themes folder on your PC. The result will be a folder with the same name as the zip file (usually!), which contains the theme files.
Step 2: Upload the new theme folder to the wp-content/themes folder on your server:
Step 3: Access your Wordpress Admin Area, go to the Appearance>Themes screen and click on the image of the theme you’ve just uploaded.

Step 4: After clicking the theme you just uploaded you’ll see a preview screen, with ‘Activate THEME NAME on the right (1 below) and an ‘X’ on the left ( 2 below).

If you don’t like the theme click the ‘X’, otherwise click the ‘Activate THEME NAME’ link.
Step 5: Check your site to see that the new theme looks OK. Note: if your new theme has a different number of sidebars (either more or less) from your old one you’ll need to re-organise any widgets you’ve used.
That's all there is to uploading and activating themes manually.
Installing Themes via the Admin Screens
WordPress also offers you the ability to search for and install themes from your Admin area. But the only themes you can install in this way are the themes that are stored on the WordPress.org site.
And that will exclude all premium (paid for) themes.
Step 1: Go the Appearance section in your menu and click 'Themes'.
Step 2: On the next screen click the 'Install Themes' tab:

You'll be presented with a screen where you can either add the name of a theme or choose specific features that you want in a theme and perform a search:

Step 3: Click 'Find Themes' and you'll be presented with themes that meet the criteria you entered:

Step 4: find one that you like and click 'Preview':

Step 5: Close the preview by clicking the 'X' in the top left corner and click the install link below your theme.
Step 6: Check the theme in your browser - and if you're happy you're all done.
If you were using a different theme previously you may need to review the placing of your widgets - particularly if you've changed the number of sidebars you're using.
OK - the next area to cover is widgets...