There are 2 ways.
1. Email . . . I am sure you already knew this one.
2. Write a script that will check for the user when he/she logs in, with the write,grep,awk,sleep,nohup commands, and have it run in the background. If you are the root of the box, you are a done deal, if you are not, you may want to ask your root what the policies are regarding users running background processes.
In addition, if you are not root, the person you are trying to send the automated message to HAS to have the mesg y set, in their environment, otherwise the command will fail.
GL
/edit: fixed small boo-boo
/edit: fixed command name