make existing WP site responsive

Hi,

I’ve been researching this, and have found some answers, but they conflict and most are a few years old, so I am not sure that the info is up to date.

I’ve been asked to update an existing (i.e. live and operational) WP site so that it is responsive. The site owners are happy with their current theme, look and feel, they don’t want anything too fancy, just screen size recognition so that it functions a bit better on mobile devices than it currently does and appropriate changes to the menu structure on small devices. With that in mind, I don’t want to change to a responsive theme, rather modify what they have.

I’ve seen advice that states I can make some changes to the html and css to accomplish this. I’ve also seen advice that there are WP plugins (both free and paid) that will also accomplish what I need to do.

I would love some up to date advice on if both of these options work well and are advisable. I am not a css expert, but I’ve worked with it a little bit so could follow a tutorial and make small changes, but if the plugin option works I would opt for that. I’ve also seen that I could use a child theme – is it correct that if I use a child theme that is responsive and make no changes, it will access the style and format of the parent, so that the site will now look exactly the same, but be responsive? This would be ideal.

I can’t be the first to need to do this, but all my searching through the forum gives me old threads – maybe most who needed this did it three years ago. I recently built my first WP site from scratch (using a very good WP theme) and it went really well so I’m hopeful with a clear path I can plan and execute this without too much difficulty. Any advice is greatly appreciated.

Thanks

will work on a Mac OS 10.8.5, but also have access to a windows 7 running an Intel Core i5-4200M CPU