In general there is no way to privately contact the users of this platform.
You can leave a comment on a post of the user you wish to contact and hope they will come back to you.
You can also use the chat rooms (https://chat.stackexchange.com/) to contact them openly.
Moderators and staff have the ability to create private chat rooms for moderation purposes. These also have to deal with issues pertaining to the site.
To get in touch with the moderators, raise a custom flag on the post, which is closest to the problem which needs to be dealt with. We will contact you through the official channels, which may include email or the aforementioned chat system. Keep an eye on your inbox.
You can also use the contact form to communicate with the staff (support) directly. You will find that on the bottom on the page (https://chemistry.meta.stackexchange.com/contact). You won't reach the moderators of this site with this option directly. This is probably the best option if you have business related inquiries.