generally the admin of the domain will add your computer to the domain to allow you to log into the domain.
you can work around this if you have domain credentials and use command to override the default logon credentials
you override the default credentials by:
logon to your local workgroup or local machine account. for example username1/passwordx
then start cmd.exe as an admin
now you want to connect to a resource called \\servername1\myshare on domain foo.
and you have a account on that domain called userx with password mommy
you would use the command
net use * \\servername1\myshare /user:foo\userx mommy
then you can use the shared resource in all the UI provided by windows.
and it will provide the domain credentials supplied rather than the un trusted local credentials.
Most people just get their computer added to the domain, and log on to the domain when they want domain access. The rest of the time they log on to the local account so they can make changes to the computer. Note the domain admin can deactivate your local accounts.