There are two domains A and B (separate forests). Sharepoint site is deployed in A domain. Is it possible to user from domain B to get access to the site?
As far as I understand Sharepoint is based on Active Directory accounts. Is it possible to have the user in both domains or are there any other alternatives?
Yes you can create cross domain access, but it requires a bit of work with the servers not code.
1.cross domain access:
You have to create a trust between the domains. Furthermore I believe you have to set up DNS, so the users (domain B) can ‘talk’ to the DNS in domain A.
The trust will mean that, users in domain B can authenticate in domain A, and find the sharepoint site. Also remember if there are firewall between the domains, this needs to be taken into account. Here you can read about setting this up, but I recommend you research more before implementing this solution: http://www.quantumofgeek.com/2010/09/configure-sharepoint-to-authenticate-cross-forest-ad-users/
2. users in both domain
If you have the users in both domains (duplicate username/password) it will still be different logon because of the domain name. And if users change their password it will not be reflected in the other domain.