How do I know when my friend logs on?

To be told when someone logs on or off you have to add that person to your friends list.
In the top right corner of your interfaces you find the button 'Add friend'.

Here you can add a username to your Friends list.

Below this button you find your Friends list.(If it is no longer there then click on the 'Lobby' option in the list on the left of your interface)  In front of each username there is an icon which tells you if that person is offline, online, idle, playing, etc.  If there is no icon then that username no longer exists.

Right click on a username in that list for options like chatting, removal from the friends list, etc.

Alternatively you can also use commands.
Type on the command bar under your Console: +notify Eendje (if Eendje is username of that person). This adds Eendje to your notify list. When she logs on you will hear 'Friend arrived'. When she logs off you will hear 'Friend departed'.
To remove someone from your notify list type: -notify Eendje
To see all usernames on your notify list type: =notify
To see those currently online type: znotl    
To get to your console click on the Console icon  on the bottom (left) of your interface.
Or go to the Menu above, click on 'View' and choose 'Console'.
  

For more options, like being notified for a titled player arriving or for games of a specific player starting, read "help notify"