The steps involved in changing your DNS service vary according to your hardware and possibly your operating system version.
Generally, you must start by finding the primary and secondary nameservers for the DNS service you'd like to use. These IP addresses are normally displayed very clearly on the service website, so, for example, Cloudflare DNS uses 1.1.1.1 and 1.0.0.1.
The simplest approach for home users is to update their router to use the new addresses. Most other devices will then pick up the new DNS settings automatically, with no further work required.
To make this happen you must log in to your router (the default password may be printed on its base) and look for the current DNS primary and secondary nameservers. Make a note of the current values in case of problems, then replace them with the nameservers you'd like to use.
If you run into problems, check out your DNS service website for any setup guidance. Keep in mind that you can also use the tutorials of other DNS providers, as long as you remember to replace their nameserver IPs with your preferred options. OpenDNS, for instance, has specific guidance for many different router types on its support site.
If router tweaks aren't right for your situation, you may have to change the DNS configuration of each individual device. Cloudflare has short and simple guidance here, while the OpenDNS website goes into more depth.