First, a little history. According to Wikipedia, it was in 2004 that Cameron Adams a web developer created a demonstration of "fluid flexible" layout. By 2008, related terms such as "flexible", "liquid", "fluid", and "elastic" were being used to describe layouts. It was Ethan Marcotte another web designer, who coined the term responsive web design (RWD) -and defined it to mean fluid grid / flexible images / media queries-in a May 2010 article in A List Apart. He described the theory and practice of responsive web design in his brief 2011 book titled Responsive Web Design. Responsive design was listed as # 2 in Top Web Design Trends for 2012 by.net magazine. Mashable called 2013 the Year of Responsive Web Design. Many other sources have recommended responsive design as a cost-effective alternative to mobile applications.
So if your website has been published before 2012/2013 you need to get hold of your website guys to change it to responsive. To be sure your website is mobile friendly go to: Mobile-Friendly Test – Google Search Console – to test your website.
If your website is managed by a developer / agency, you can have them make a responsive WordPress theme for you, one based on your current theme. But most themes today have the responsive option.
On the other hand, you are managing your own website and using WordPress, head over to your WordPress dashboard and under 'appearance' click on 'themes' and then click on 'install themes', and in in the search box you want to put in the keywords 'responsive'. This will bring up all the themes that are responsive then you can choose the one that's best for your site. After the necessary tweaking, you have it, a responsive – mobile device friendly website.
Nowadays for new websites, the majority of available platforms are made responsive so they just need to be tested for their effectiveness.
You might then want to check if your site loads quickly on mobile devices. There are two steps you can take to make your mobile devices load quicker. Head over to your plug-ins area and click on 'add new', then look for and install something called 'WP Smushit. What this does is, it compresses your images. Loading of images on mobile devices is usually 80 percent of the time. So if you can reduce your image sizes, you can reduce the loading time for a mobile device significantly. Making your site load very quickly so that people with mobile devices can see your content without having to wait.