Under construction (diversion of traffic)

I am wanting to make some pretty extensive ‘repairs’ and reconstructions to my site, particularly to the layout etc. Whilst this is completing, is there a way of diverting traffic to either a) another page, or b) more specifically an ‘under construction’ page so that readers don’t end up loading a version of my site that’s in a mess while the ‘work’ goes on?

I note that there is the option to mark the homepage as something different to the root page, however this will mean that my current site header, with all the links will be on the page that my readers are diverted to, meaning they may still be able to get to pages while I am making changes. I don’t want this to happen if possible.

Can somebody explain how I could do this in layman’s terms, seeing as it is obvious that I don’t have much of an idea as to what I’m talking about…

Cheers.