How to logon to a computer using dailup connection

As I interpret your question, the computer you are connecting to via a dialup connection would need to be running a remote access service and have a modem installed. For Windows, the server versions include such functionality, the client versions (XP, Vista etc.) require a 3rd party software solution like PCAnywhere. If both machines have Internet access Windows' native Remote Desktop Client can be used (no modems needed). See Remote Access Overview for Windows Server 2003. For Linux or other OSs, Google "[insert OS here] dialup remote access" for a plethora of walkthrough tutorials on setting up a PPP remote access server.