Reading the install instructions it looks like I should put the grav folder inside /public_html
If I do that, how do I get the site to come up at mysite.com and not mysite.com/grav ?
You should but the contents of the Grav-folder (which you downloaded, includes bin, cache, images, logs, system, user, vendor-folders) in the site-folder, eg. mysite.com.
Thanks - I did that earlier but I must have missed something. This time it worked.