There are some ways for doing that
one way is sending user credentials(encrypted) to other site and by using an http module in destination try to login to the application but it is not Secure.
the other way and the secure one is using WIF(Windows Identity Foundation) and with that you will have SSO(Single Sign one and Single sing out) functionality. Using WIF SDK make the life easier because it generates the required configuration in both sides and authentication happens only in IdP(Identity Provider) side.
http://www.microsoft.com/en-us/download/details.aspx?id=4451[
^]