localhost vs live?

I’ve been dabbling in WordPress for awhile but now I want to get a little more hands-on and I’m confused about what the normal process is. What I’ve been doing is using ThemeSwitch (plugin) to work on themes before I activate them, but what if I want to do a lot more? What if I want to change settings and play around with widgets and who knows what else, but I don’t want it to affect my production site until I’m done with all of it?

It seems like this is the point where I need to start using the localhost. I found some tutorials for installing WordPress locally, but no details yet on what you do once you’re done working on it. How to push it to your web server? Or how to put your current database onto your localhost? And when you do, how do you restore the changed database without losing whatever posts you published since then?
I have some other questions about this whole process too but let’s start with that for now ??

Thank you!