Step one is make sure the licensing agreement for a font allows this use. Many do not and they’re fonts that are for printed media only. If it is an allowed use, then next phase is purchasing or downloading it. This is usually specified as a “web font” licensed use. DO NOT screw that up – people will sue you. In this font you’ve mentioned the use is a “pay-as-you-go” 4 year web license. You have to re-up after that… It is also licensed on a certain number of page views (250,000 by default)… So you might have to re-up even faster than that.
Copy it into a folder on your web server or host it in s3 or something.
Use link element or import statement in CSS to apply the font. You’re not going to link to Google, you’re going to link to some sort of relative location on your server that points to the font package. Make sure your body text has a valid font-family line and plenty of similar fallback fonts.
People who visit your site will have to download the font into their browsers cache. Since you aren’t going to be Google or something this will always be slower than using a Google font, or similar.
Once you get past step #3 it’s no different than using any other font. But, as I stated make sure you are using fonts that are web use licensed that’s the only place you can really screw up. Don’t think you’re going to mess with these companies either as most of the font sites make a ton of money and love to send you DCMA shutdowns for bootlegging their fonts.