This is a fairly common problem, but for most people it can be resolved within a few tries. The most common causes are..
Mistyping your password. Oddly enough, this produces an error like "connection failure" or "connection timeout." Type it carefully and make sure caps lock is off. Or get rid of the password and see if this fixes it.
A version mismatch between the client and server. Ark is updated quite often. On the server listing page, we say either "Up to Date" or "Needs Update" next to your server version number. You can force your server to get updated by restarting it.
A network problem on your end. Reboot your router and your computer, and make sure Steam is running and not reporting any connection errors.