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Requirements:
To run WordPress your host just needs a couple of things:

• PHP version 4.2 or greater
• MySQL version 4.0 or greater

Create a Database
You can usually do this in your hosting control panel. If you aren't sure how to do this, ask your hosting company. After you have set it up, you should have 4 pieces of information about the database.
1. Database Name - The name of your database.
2. Username - your database user name.
3. Password - Your database password.
4. Host name - This is going to be a host name. It might be something like mysql.mydomain.com, or just localhost. Without these 4 things, you won't be able to set up WordPress. Again, contact your hosting company's tech support if you have any trouble with this.
Download the current version of WordPress.
This is easy. Just go to wordpress.org/download/, and download the current version. You have a choice between the ZIP file or the TAR.GZ file. I think the TAR.GZ file may be smaller, but I always download the ZIP.
Uncompress the WordPress ZIP file.
Again this is easy.
Configure WordPress
Open the WordPress folder and rename the file wp-config-sample.php to just wp-config.php. Now open it and insert the 4 pieces of information about your database into the 4 fields below.
Change:

define('DB_NAME', 'wordpress'); // The name of the database
define('DB_USER', 'username'); // Your MySQL username
define('DB_PASSWORD', 'password'); // ... and password
define('DB_HOST', 'localhost'); // 99% chance you won't need to change this value

to

define('DB_NAME', 'yourDatabaseName'); // The name of the database
define('DB_USER', 'your-username'); // Your MySQL username
define('DB_PASSWORD', 'your-password'); // ... and password
define('DB_HOST', 'your-hostname'); // 99% chance you won't need to change this value

Choose Your Install Directory and Upload Everything
If you want your WordPress blog in a separate directory of your website, like “yourdomain.com/blog”, then rename the “wordpress” folder to “blog” and upload it to the root directory with an ftp program.
If you want your blog to be in the root directory of your site, meaning the blog will be located at “yourdomain.com”, then just open the wordpress folder and upload all the files and folders into your web root. If you already have a file called index.html, or index.php, you'll need to rename it or get rid of it before you uploading everything.
Finish and Install

8. In a browser, go to the domain where you uploaded WordPress, and then to /wp-admin/install.php, and follow the simple directions there.
You will be given a username and password. Save it in a safe place.
That's it. You now have a new blog. You can now log in with your username and password, and start writing.
Download a WordPress theme
This is the fun part. Picking a WordPress theme. There are many places to find WordPress Themes. When you find one you like, just download it and unzip it just like you did with the WordPress ZIP file.
6. Add Your Theme
You can do this after you upload, but it's probably easier to just do it now.
Look for the themes folder. It's in the wordpress => wp-content => themes.
There should already be 2 theme folders in the themes folder, “classic” and “default”.
Just drop your new theme folder in with them. (remember, it must be unzipped first)