To be clear, 'Cypress' and 'Cypress Cloud' are not the same thing.
If you are not sure how to get started with Cypress then check out this:
https://docs.cypress.io/guides/getting-started/installing-cypress
It needs to be installed via npm (install node package manager first:
https://nodejs.org/en/)
Once you install Cypress then you can start figuring out how to create tests, this is a fantastic starting point:
https://docs.cypress.io/guides/end-to-end-testing/writing-your-first-end-to-end-test
Regarding Cypress Cloud, it is a feature-rich dashboard for stats regarding your test executions. It used to be called Cypress Dashboard which I think was a clearer name tbh, but anyway it got renamed 🙂
Be sure to read all the documentation under cypress guides, it explains a lot of stuff and also introduces many best-practices which are super important.