The oxygen in the chain divides the chain into two pieces, with each piece having its own name.

methyl ethanoate

The left hand side has only one carbon, so it is a meth.
A yl is added to meth.
This side is called methyl.

The right hand side has the other =O.
This side is called the ...oate side.
This is easy to remember... the side with the O is the Oate!

This side has two carbons, hence ethan.
The right hand side is ethanoate

Put the two pieces together, and the name is:
methyl ethanoate