This is a very broad question. Moreover, it is generally a pretty bad idea, SEO-wise, to have multiple independent domains that each serve the same content.
Logging in is generally either done through Cookies, or through extra parameters in the URL. Cookies are always domain-specific, for obvious security reasons. If you want to ensure folks will be logged in to all the domains at once, you can create an internal purpose-driven domain to handle authentication (without such domain showing in URL bar, and only being used for HTTP redirects, effectively); such domain will store the login state for all the rest, and the rest would pick up the login state through such purpose-driven domain (through HTTP redirects).
In general, however, this sounds like too much trouble. Consider that, perhaps, some users specifically want to use different domains for different accounts, so, you'll effectively break their usage if you mandate that a single login be used for all of them. And, back to the original point, doing this is pretty bad for SEO, so, just don't do it.