Honestly, just using the basics of "responsive web design" (search phrase) is most of it. That is, implementing your site using CSS media queries to adapt your layout across multiple device sizes. Contrast that to using hacky device detection to deliver some entirely separate and "mobile-specific" site. One anti-pattern that often happens is the "mobile" detection is wrong, and delivers some phone-sized UI to a tablet. Instead just leverage CSS to make your site look good at the user's current display width, whatever that is, without having to know anything about the device. This is also great for desktop users, e.g. who might have your site in a browser side-by-side with something else, or similar.
All of the "evergreen" browsers have a mobile design view built into their dev tools these days. You can enable that, switch between specific device screen profiles, and continuously drag the "screen size" handles to watch your site's behavior at different sizes. This is great for development, since your web inspector view stays at full size.
Combining CSS media queries with CSS flexbox is a hugely powerful way customize the end-user experience for different devices. Flexbox not only makes basic layout adaptations straightforward (or free!), it lets you handle some otherwise tricky cases using tools like reordering support.
It's probably also worth searching for "mobile first web design" for further resources.