Emacs 24 normally works very well with Tramp. What you might need is ControlMasterAuto
in your .ssh/config file. This will ensure that the ssh connection information passes seamlessly to Emacs. This will also ensure that you only need to login once in a terminal and use multiple emacs frames in tramp mode. I have detailed the following steps
(1) Go to your .ssh/config file and add the following options
Host <hostname>
ControlMaster auto
ControlPath ~/.ssh/%r@%h:%p
ServerAliveCountMax=30
ServerAliveInterval=5
(2) Now login to the remote host through terminal.
(3) Open emacs frame and try opening the remote files through tramp (/ssh:). You must be able to connect to the remote host.
The above steps should work even for a two level authentication (using a rsa key +password).