The major player in the blog game is WordPress, a content management system (CMS) that powers millions of websites, including The New York Times, Quartz, and Variety. WordPress-powered sites are incredibly easy to set up, customize, and update—ideally on a daily basis. You aren't required to learn fancy-schmancy FTP tricks (though you can certainly use them if you like), and there are ridiculous numbers of free and paid WordPress themes and WordPress plug-ins to give your website a pretty face and vastly expanded functionality. Though WordPress dominates the blogging space, it isn't the only blogging CMS of note, however.
One factor that may influence your choice is the decision on whether to use SSL for your website. A site that uses SSL will have a web address starting with "https://" instead of "http://". In ancient times, webmasters typically only bothered to use it if they were selling goods and services and needed to collect credit card numbers, or if they had some sort of facility that required their visitors to log in with a password.
When your website is ready for public viewing, you'll have to upload your webpages to your web server. You can buy space on a server from various providers (see How much does it cost to do something on the web?). Once you settle on which provider to use, the provider will email you the access information, usually in the form of an SFTP URL, username, password, and other information needed to connect to their server. Bear in mind that (S)FTP is now somewhat old-fashioned, and other uploading systems are starting to become popular, such as RSync and Git/GitHub.