Cloudflare is a service that can be used as an proxy to ones webhosting.
One just point domain to cloudflare nameservers, configure DNS in Cloudflare panel and Cloudflare will comunicate with webhosting to deliver webpages to the visitors.

VISITOR - ISP - DOMAIN REGISTAR - CLOUDFLARE DNS - CLOUDFLARE <-> WEBHOSTING
(visitor see webpage like it is hosted by cloudflare, but cloudflare anonymously getting website from webhosting)

How to proceed?

Create account on Cloudflare and add a website.
You will be asked to change your domain nameservers to the cloudflare ones (contact your domain registar if you dont know how to change).
Once changed, confirm that you did the change in Cloudflare panel.
Then CLoudflare will try to detect DNS values.
If it do not detect anything, you will need to add these:

A - yourdomain.com - theIPofServerWhereWebsiteIsHosted - 2minutesTTL
A - www - theIPofServerWhereWebsiteIsHosted - 2minutesTTL

that is all needed to instruct CLoudflare which server to contact in order to deliver website to your domain visitors

The DNS changes may not reflect immediatelly thanks to your internet provider DNS caching.
After like 30 minuts, you check your domain on www.intodns.com and if it appears it correctly points to cloudflare nameservers, you can try to access your website via web proxy to check whether website is working (DNS configured properly).

Example web proxy: www.anonymouse.org

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If you use domain for e-mailing, check DKIM, SPF record:
Once site is served via CF, you can try to send an e-mail from your CF protected domain to your other private mailbox to see if also SPF and DKIM - DNS records (if you use them) works/pass the test, one can see it in such e-mail headers. If dkim=fail, remove all spaces and quotation marks from DKIM record in cloudflare and remove backlash at the end.

Related reading: How to prevent IP leak thanks to MX mail record - https://internetlifeforum.com/mailserver/6681-how-setup-mailserver-stop-ip-leak-when-using-cloudflare/