So if your website has been published before 2012/2013 you need to get hokd of your website guys to change it to responsive. To be sure it is mobile friendly go to : Mobile-Friendly Test - Google Search Console - http://dovetanet.link/mobildc72 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 the search box you want to put in the keywords ‘responsive’. This will bring up all the themes that are responsive ten you can choose the one that’s best for your site then after the necessary tweaking, you have it, a responsive - mobile device friendly website. For new websites, the majority of website platforms are made responsive so they just need to rest them for effectiveness.
Then you might want to check if your site loads quickly on mobile devices. There are two steps you can take to make your mobile devices load more quickly. 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 images 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.