New to WordPress, how do I give a client a website I’m confused?

If they have a WP website and need minor changes and the client doesn’t want to approve them before publishing them, make them directly to the website.

If they have a WP website and want major changes, copy the website to a subdomain of their domain either on your hosting (preferably) or theirs and make the changes there. Then get approval and migrate the changes to their live site.

If they don’t have WP, you’ll use basically the same approach but you’re going to have to evaluate what technology their site requires and set up a development/staging environment accordingly.

>1. If they have a wordpress website, is it best practice to just ask for their login details and work from there? If not, how can I make them a better website under the same domain they already have?

If they’re hosting it, then you’ll eventually need access to their cPanel or host. But don’t share credentials. Rather, ask them to delegate access, or make you a user, or whatever the host calls it.

>2. If they don’t have a wordpress website how do I edit their current website? Do I have to make a new domain with new hosting?

If they want edits to a non-WP site, then figure out how the current site was built and find someone to edit it, assuming you can’t. If you’re building a new site anyway, build locally or on a subdomain, then just migrate it to the existing or new host. You don’t need a new domain, you just need to point the A record to the new server.