To buy a domain and host a website, start by choosing a reliable domain registrar. Search for an available domain name that reflects your brand or purpose. Once you've selected a domain, proceed to purchase it, considering factors like renewal fees and privacy protection. Next, choose a hosting provider that meets your website's needs in terms of storage, bandwidth, and security features. Purchase a hosting plan and link your domain to the hosting account. Configure DNS settings and upload your website files to start sharing your content online.