How can I place a signup button on homepage?

The Header links in OSQA are kept in a separate registry, which can be modified at forum.registry. If you explore that registry you'll find a HEADER_LINKS section. If you want to add a "sign up" link to the header, this is the file that has to be edited.

A good example of this functionality is the "Login" link. Take a look at it:

ui.Link(
    text=lambda u, c: u.is_authenticated() and _('logout') or _('login'),
    url=lambda u, c: u.is_authenticated() and reverse('logout') or reverse('auth_signin'),
    weight=200),

But it's not a good idea to edit the Python files of your project, especially if you're planning to update your system frequently. Another option is to edit the template files, that are kept in forum/skins/default/templates and specifically the base_content.html file. Before showing the link you can do a simple check using an if-statement.

{% if not user.is_authenticated %} ... {% endif %}

In general, this are the two options.