To start dropshiping business you will need a domain name.You can go to godaddy.com and register a domain name of your choice you can also buy expired domains for better seo.
Now there is two choice,You can chose one.There are two main CMS (Woocommerce and Shopify)who are providing dropshipping management.
For Shopify you can just go to shopify.com and register for a package of your choice.Please note Shopify is much costly than woocommerce (WordPress).
Setting up or connecting shopify with your godaddy domain name is very easy.You just need to click on connect my domain and chose the provider as godaddy.put your credentials and the shopify will automatically connect with your website with auto name server configuration.
For wordpress website you need to purchase a hosting package from any host I specially like bluehost and namechecp hosting.
After selecting a hosting package you just need to connect the domain with the hosting name servers.After your site become successfully propagated you can install the wordpress from cpanel of the hosting.
Choose a theme(You can go with paid themes like flatsome and others, these paid themes are really good and make your work lot more easier)
Now come to the most important point that is dropshipping plugins:
In shopify you will get a plugin called oberlo,Which will help you to import product,auto price and stock update,auto order fillup and more.
In wordpress you need to purchase a plugin called alidropship.this plugin will cost around $ 80 but it is a one time payment.