For a first-year student your problem can indeed be rather daunting, as it requires the combination of several reaction types.
Your first step, Michael addition between enolate and unsaturated ketone is correct. For the second step, I guess you have seen the wiki page on mesityl oxide, which shows what happens next. In your case, the enol attacks one of the ester groups, after which ethoxide is expelled. This gives you the six-membered ring and the second ketone.
The final step, removal of the remaining ester function, doesn't happen in situ (I think, I'm a bit rusty on this), but if you know what a beta-keto-acid is and what it does, you should be able to work it out.
As for the use of ethoxide as base, this is just to eliminate any transesterification reactions. Strong non-nucleophilic bases (tertiary amines and such) can also be used, depending on the exact nature of the reaction. What to use when is something you'll learn as you go along.