Using tee to create a log

I have a command line utility that spits out data on the screen as it runs.
I want to capture this data to a "log" file so I can read it later. I
have been told the tee command will do this for me but I can't seem to get
the command line correct as the log file is always empty.

The man and info pages are not very helpful to me since I am just learning
this piping commands stuff.

Alan