There is no point in reinventing the wheel. If you have gone with Siteground – they have excellent support and training resources on this part and I don’t think I could give you better information. Now there are a few ways of doing this. You should (as a new user) be prompted by a Siteground Wizard asking you if you want to install WordPress. Details of the wizard can be found here: https://www.siteground.com/tutorials/wordpress/siteground-wizard-install/
I have not been able to do this step by step guide for you, as I have had my account for a long time and I have many domains already installed on my account. If you are not presented with the pop up, it is not a problem. This is how I do my new installations: https://www.siteground.com/tutorials/wordpress/softaculous-installation/
If at any point you get stuck or have any problems, just pop on over to Siteground Support via the chat.
First click on “Support” on the main menu ribbon from your customer area.
Scroll right down to the bottom of the page, and click on the option to contact the team.