The mines can be hard to locate when you first start playing and actually took me a bit of time to find- and at that I stumbled upon them by accident. In order to open the first mine all you have to do is go to the excavation site (with Flora and Carter) carrying your hammer after 9:00pm. It doesn't always work on the first try, if it doesn't exit the site and walk back in 10 minutes later until it works. Carter will enter and say "There you are Stinky (Stinky is what I named my character). I was hoping you could help me with something. You see I found sort of a tunnel here." He'll ask if you have your hammer, you'll nod and he'll show you the spot on the wall where you can smash open an opening to the first mine. In this mine you'll find Junk Ore, Copper, Silver, Gold and Mystrile. If you wish to open the other mines simply reach the bottom level of the current mine you have open and then re-enter the site at night again. Note: The first mine only has 10 levels, but as you progress they'll get deeper and deeper. The second has 255, The third has 999, and the last has 60,000 I believe. I haven't made it half that far yet, so I'm not quite possitive.
If you have any further questions about Harvest Moon DS, feel free to leave a message on my message board.