just briefly here:
When you look at the finished front or the sketch thereof: the arm holes start somewhere lower than the V-cut but their shaping is not entirely done before the V-neck starts. That is normal. Therefore one shaping goes on while the other starts. They happen in different places so just think about what you want to achieve and it will make sense.
Now you work row 1 of the V-neck: it is a right side row. So when you hold up your work your see the outside of the vest.
find your middle stitch. Put it onto a saftey pin and leave it there. It will be used for a ribbingband in the neckline or something later on.
Now you work that row to the end.
Once you work back (doing with the armhole what ever it wants you to at that point) you work no further than to that safety pin ever again. the stitches for the left side (seen from right side) get worked until the shoulder is done. THEN you get back to the other side and work those stitches. you finish your shoulders seperately from here.
Follow the instructions for the shaping as they go.
what you want to end up with is the following:
right side lies on a holder or spare needle for now (mostly you will take the stitches off your working needle. I sometimes just leave them there, though).
the left side you work back and forth. on the outside (the left side of the left side) you work your shaping for the armhole just as you did on the back of the piece. You can lay things ontop of eachother to check if you go correctly.
on the right side of that left side you work the V-neck (that is the middle of the vest). That means you decrease bit by bit to make the side smaller and smaller. Essentially you end up with as many shoulder stitches as you had on the back. (just on the back you worked to the neckline and probably bound off a bunch of stitches in the middle.)
Once you finished that one side, do the same thing with the stitches on the right side.
you join your yarn in the middle (next to the stitch on safteypin) and work a row on the wrong side first.
On that right side work your armhole decreases and the neck line as your pattern says.
I hope I could help.