First, be sure you are running WordPress 5.0 or newer. If you are, the Block Editor (a.k.a. ‘Gutenberg’) is the default editing experience.
If you are running an up-to-date version of WordPress, and you are still seeing the Classic Editor, that’s likely because the Block Editor has been disabled.
There are several ways to disable the Block Editor. It’s possible you (or another administrator on your site) has installed and activated the Classic Editor plugin. Or, it’s possible that a plugin or your current theme has disabled it via code.
If you have the Classic Editor plugin installed, you can enable a setting that allows you to switch between editor modes, essentially choosing which editing experience you would prefer on an individual basis.
Hopefully, this helps you track down the settings for your own website so you can toggle between the two editing experiences.