Getting In

Make sure you either have cPanel/Plesk Login access or an FTP manager like Filezilla already setup and connected.

What and Where

In the root directory (httpdocs, public_html) of your website will be a .htaccess file, locate and edit this file.
Add the following code:

<IfModule mod_deflate.c>
AddOutputFilterByType DEFLATE application/javascript
AddOutputFilterByType DEFLATE application/rss+xml
AddOutputFilterByType DEFLATE application/vnd.ms-fontobject
AddOutputFilterByType DEFLATE application/x-font
AddOutputFilterByType DEFLATE application/x-font-opentype
AddOutputFilterByType DEFLATE application/x-font-otf
AddOutputFilterByType DEFLATE application/x-font-truetype
AddOutputFilterByType DEFLATE application/x-font-ttf
AddOutputFilterByType DEFLATE application/x-javascript
AddOutputFilterByType DEFLATE application/xhtml+xml
AddOutputFilterByType DEFLATE application/xml
AddOutputFilterByType DEFLATE font/opentype
AddOutputFilterByType DEFLATE font/otf
AddOutputFilterByType DEFLATE font/ttf
AddOutputFilterByType DEFLATE image/svg+xml
AddOutputFilterByType DEFLATE image/x-icon
AddOutputFilterByType DEFLATE text/css
AddOutputFilterByType DEFLATE text/html
AddOutputFilterByType DEFLATE text/javascript
AddOutputFilterByType DEFLATE text/plain
AddOutputFilterByType DEFLATE text/xml

BrowserMatch ^Mozilla/4 gzip-only-text/html
BrowserMatch ^Mozilla/4\.0[678] no-gzip
BrowserMatch \bMSIE !no-gzip !gzip-only-text/html
Header append Vary User-Agent
</IfModule>

Test, Test, Test!

Save, the page then immediately test the page, if you are shown a 500 error, restore your backup file.

Then Test its working here: https://checkgzipcompression.com/