What is your new website for?
I know it sounds obvious, but before you start developing your website, it is a good idea to reflect on what you aim to achieve by having a website. This will help you work out what resources; time and money, you are prepared to invest, and is a first step in the overall design.
I am not going to go through the server setup process for WordPress. There is plenty of information elsewhere on how to install WordPress and configure your server. Setting up servers is usually done by your service provider or systems administrator. Most service providers offer the facility to install WordPress through their control panel using a wizard. If your provider does not offer this there is the WordPress Famous 5-Minute Installation which is a simple set of steps to get WordPress up and running.
WordPress is installed with a number of free themes and plugins. Your service provider might also include their own additional plugins. If your site is on the Internet, it is now active on your domain name (e.g. www.your-domain.com; see Basic Overview for an overview).
You login to your WordPress site through the login page (e.g. www.your-domain.com/wp-login.php) using the name and password you chose when you installed WordPress. Once logged in you will see the WordPress Dashboard.
If your site is on the Internet you might want to have a place holder displayed to the public while you work on your site. I currently use the Under Construction Plugin by Web Factory ltd. It is simple to use and does the job. To do this you need to install the plugin. Many plugins can be simply installed from the Plugins page of the dashboard. Click Add New and then search for Under Construction Plugin. Click Install and then click Activate and you are ready to set up your under construction page. To set it up click on Settings on the plugin listing; or select Under Construction from the Dashboard Setting menu.