The quickest and easiest way is using this free Mobile Friendly testing tool by Google. Just enter your URL and it will show you the results as well as a screenshot of how your site appears on a mobile device.
Open Google on your mobile device and search for your website or blog. If your site is mobile friendly there will now be a gray “mobile-friendly” notice underneath each URL in the description snippet. To see all the indexed pages of your site then search for site: yourdomain.com instead and check if all pages on your website/blog are mobile friendly.
Check the site yourself on a mobile and tablet device, testing the different features and pages. My advice is to write down a list of anything that isn’t working correctly or looking right so then it’s easier to go through the list and correct it.
Check the Mobile Usability section of Google Webmaster Tools. It will tell you a list of things that can be improved on your site to help optimize it for smaller devices. Even if your site passed the mobile-friendly test, there may still be errors and it’s best to fix them.