Training should be part of belonging to the "well-regulated militia". How can the militia be well regulated if members are not trained in the basics?
Nothing is stopping training from being part of a well-regulated militia. However, the second amendment does not require one to be part of a well-regulated militia in order to have the right to keep and bear arms.
Actually, it can be argued that the 2nd specifically refers to members of the militia being armed. "People" can also be interpreted as the people as a whole being allowed to maintain a militia to represent and serve them.
Sure, you can argue that, but it's not all that strong of an argument, and it's not one the Supreme Court has agreed with.
I think the second amendment was poorly written. I wish it hadn't mentioned the militia, or had clearly linked the militia to the right, whichever was the intent. Unfortunately, that isn't what we got.
I think a decent analogy would be if an amendment were created enshrining the right to cell phones, written something like this: "A high-speed, reliable phone connection, being necessary for the communication of a nation, the right of the people to own and use cell phones, shall not be infringed." Under that amendment, while it certainly says that a high-speed, reliable phone connection is important, it doesn't say that owning a cell phone requires such a connection.
Regardless, I believe the courts have ruled that the second amendment is not limited to members of a militia.