When you open the DMG, you should get a new window. In that new window you should see the MC application and a shortcut to the Applications folder. Both of these in the same window. You might need to resize that window in order to see both clearly; in some recent builds the Applications folder is part way off of the screen until you make the window taller.
Your reasoning on what to do is correct. Drag the new MC app into the Applications folder. Sometimes it's tricky to get MC to drop correctly into Applications. When you are "on target" you will see a green highlight with a + mark in the center. If you release the mouse button when you see this, it should copy over into your Applications folder. However, since you have an older version installed, Finder will ask you if you want to keep the older app, or replace it. That's up to you, but you definitely have to answer one way or the other, or nothing will copy.
Good luck to you!
Brian.