search for: hostname_date_tim

Dear All, I am a newbie in the unix world. I have a problem. I try to log all my typed, edited (via vi/vim) and of course the output/result of a command into a file (specific file e.g.: hostname_date_time.log into my home directory). I would like to reach the same logging what the putty does. But I do not want to use putty under linux. This is why I ask you is it possible to logging the ssh as the putty? I read the related man pages and look after my problems in the net as well (forums, etc). Unf...