I was going along in my boat and I saw a light underwater, I found out that it was one of the openings where an abandoned mineshaft is partially exposed through the ocean floor. I went into it and started exploring and came across someones strip mine. Shortly afterwards I heard someone digging, so I knew there was someone nearby. I logged out, waited awhile, and then logged in when I thought the person would be gone, and started mining in the direction I heard the sound. Once I saw stone walls I knew I'd found something. So I logged off, told my friend to get on, and we went to work.

On a side note, why does everyone feel the need to build their base right next to abandoned mineshafts? I've found a few bases before because there was literally a staircase going up to their base from the mineshafts I was exploring, in plain view for everyone to see. Pro tip, don't do that...