How can I contact another user, if that user has not specified any contact details in their profile?
Just go to chat.stackexchange.com and go to the targeted user profile : Then change the room parameters to make it private (or Gallery if you don't have enough reputations) inside the room parameters.
Instant messaging or private messaging is not available: requests to implement that have been declined to keep focus on questions and answers, and to keep those visible to everyone.
Some users are active in chat.
In rare cases where immediate action is necessary (e.g., the user has accidentally left login credentials in a post), you can flag for moderator attention and explain what the urgent matter is about.
On the flip side, if you want to provide a way for people to contact you, leave contact information in your user profile.