New site & Url, same old server. How do I direct traffic?

I have created a new site at a new domain and would now like to direct my old url to the new URL. Both are WP sites…

I’m pretty sure I know how to do that (via the hosting server), but I also want to leave up my old site to copy content over to the new site over time. I’m too busy now to do it all at once.

Some things I have done that might make it more confusing…(or at least to me b/c I don’t know much in the way of code)

Both sites are hosted by the same server company (1and1). the old site is at from the root directory, the new one has it’s own folder I named ‘b’.

I also now have 2 Word Press accounts & installations. I’m not sure which version the old site is, but the new site is 3.7.1

So how do I direct ‘www.a.com’ to ‘www.b.com’ while still being able to go into http://www.a.com’s WP admin panel to copy content? In the end I’d like to move all of ‘b.com’ to ‘a.com’ eventually, but if it’s easier I can live with a permanent redirect as the old site really isn’t tweaked for any special SEO stuff.
Thank you for the help, and the more basic the better…