I have the same question. I just began employment at a new place where I will be updating our page as well. I am familiarizing myself with concrete 5, but cannot find information about how to build a new site while maintaining the current live page.

You just need to adjust your css files to be 'responsive'.

What version of C5 r u using?

What theme r u using?

As with most things web development, there is more than one approach. Which is best for your circumstance depends.on the specifics of your site and needs.
-How big is the site
-What is the current design
-Do you have new content, and/or how much of the existing content do you want to use?

What is "easiest" depends on your experience. Saying you are a "beginner" is somewhat vague but probably limits your options. Just how much of a beginner you are can make all the difference.

As with most things web development, there is more than one approach. Which is best for your circumstance depends.on the specifics of your site and needs.
-How big is the site
-What is the current design
-Do you have new content, and/or how much of the existing content do you want to use?

What is "easiest" depends on your experience. Saying you are a "beginner" is somewhat vague but probably limits your options. Just how much of a beginner you are can make all the difference.

I can't find what version of C5 I have but when it checked for updates there weren't any. The theme that I'm using is Plain Yogurt and when I tried to change it to Greek Yogurt for mobile it didn't work very well, some parts changed others didn't. Probably the code that I had put in.

My nav bars are a mess and I'd like to change some of what it looks like, probably change the home page too. I'm thinking of going with either Fundamental or Backbone theme.

Yeah, different themes often use different names for areas (although that probably isn't the case between Plain Yogurt and Greek Yogurt, but I haven't checked), and any content in an area of the old them where that area doesn't exist in the new theme will not show up, so that must be dealt with. Sounds like you added additional stuff that didn't get included.

If you want your new site done with the latest version 5.7+, that will require a complete rebuild because there is no upgrade from 5.6 sites (and hence you can't just switch to a new theme). But on a simpler site such as yours, that's not such a big deal.

I think either of those themes would be a good choice (based on the developer of those).

Sounds like you're running 5.6 because 'Yogurt' is not in 5.7, nor is backbone.

Do a fresh install of 5.7 and go from there.