If you don't belong to Ravelry this might be a good time to join. It is free and I think you'd get good help there. I don't have this pattern, but maybe someone here does. On Ravelry I see over 300 people have made this coat and you can read their notes and ask questions directly to folks who have made it if you want to.
If you don't want to go that route, can you give the hood part of the pattern, or at least the row where you begin the hood? I looked on Ravelry and saw pictures of the coat (very cute) and see that a lot of people left the stitches live at the top of the body pieces and used them instead of picking up stitches. It sounds like to do that you may have to increase up to the number called for for the hood. If you want to pick up stitches, it sounds like you need to pick up stitches across the top of each of the body pieces, and use them to make the rather oversized hood. Does it tell you to sew the body together before picking up stitches for the hood? It seems like it should.
There is a video here about picking up stitches. It is not real hard, it is kind of like knitting into the edge, pulling each new loop up and onto your needle. The place you put the needle for knitting up the loops is close to the edge, but not right at the edge (there will be a bit of a seam formed). You can experiment with exact placement. The way it looks as you work it is the way it will look when it is done. If it doesn't look right you can take out a few or all of the new loops and try again, you want to achieve a smooth, nice looking line.