You can use the rsh command. Check the man page, but in general you have to tell the remote machine to trust the source machine to have already authenticated the user.
You do this by putting the source hostname and the source user name, in the file $HOME/.rhosts on the remote machine for the user whose account you will log into.
Notice that the remote host will get the source host's IP address from the socket connection. It must be able to do a reverse lookup on this address to find the source host's name.
So for example, I have two machines, machone and machtwo, and I want to run a script on machone that will run a program on machtwo. I put the following in my .rhosts file on machtwo:
machone ptpage
There are other ways toconfigure this. hosts.equiv(4) will give more info.
Be aware that if the source machine is Windows, it will usually deliver the user id in uppercase. Also you will want to be sure that you actually trust Windows to do the authentication. Depending on the configuration, it's often possible to pretend you're someone else.