Enable compression
Compressing resources with gzip or deflate can reduce the number of bytes sent over the network.
Google Pagespeed gives me the above recommendation for making my website load faster. I'd love to do this, but I'm not sure how I go about doing it. Do I locally compress the files then upload those? Or is it a server-side thing?
If so, am I still able to edit the files easily? Or is it in compressed jargon?
It is a server-side compression. Please read online more about gzip compression, so you can understand it properly. It uses your server resources, so not in all cases is it recommended.
This can be done with .htaccess easily. You can read about enabling it on an Apache server here: http://www.techiepark.com/tutorials/how-to-enable-gzip-compression-in-apache-server-to-speed-up-website/
Best way to do this is to contact your server administrator. They can also have good advice concerning your server setup & site resource usage.