The armhole and shoulder need to be sewn in one manoeuvre, It looks more tricky than it is. I find it helps to lay the shirt out flat as pictured above, once everything is sitting where it should, you can pin the front and back shoulder seam closed. That is as much as you should pin, don't attempt to try and pin the whole armhole.
Turn the shirt over so you are looking at it with the back yoke sitting on top of the front. Start at the neck and sew a 1cm seam down towards the end of the shoulder. (note for later: *When you sew the other sleeve, have it facing the opposite way around - so the front yoke will be sitting on top. Still start from the neck edge*)
Stop at the end of the shoulder EXACTLY 1cm away from the edge of the shoulder and keep your needle down. Don't back tack or cut thread. Keep the needle down.
With the needle still down, the piece underneath will need to be snipped very carefully with sharp scissors. Cut a small straight line from the corner of the underneath piece stopping 1mm away from the needle. Be careful not to cut anything else here, it should just be a single layer.
Now that you have released the seam allowance by clipping in to the needle, you should be able to release the underneath corner by gently rotating it until the edge of of the fabric now lines up directly in front of you in a straight line as you would normally line your fabric up.
Still without moving the needle from its down position, gently rotate the top layer so the edges meet each other and line up in front of you. You will notice on the armhole there are notches. The single notch on the armhole should match up with the yoke seam, and the double notches on the armhole should match the double notches on the back body. You could pin the two layers together at the notches now they are in place if you need to.
Continue to sew the sleeve into the entire armhole all the way around, noticing that the sleeve finishes at the end of the front armhole.
Check that the seam is sewn nicely (double check the shoulder corner as its easy to catch something you didn't intend to) and then overlock the edge of the seam to tidy it up.
Now it should look something like this and you should be left with just the underarm to finish off.
Sew the underarm seam closed with a 1cm seam from the cuff and sew all the way to where you finished stitching on your front yoke earlier, ensuring there are no gaps or holes and the whole seam is securely closed.
If you haven't noticed - the fabric grain for the front underarm seam is on the straight grain, the back underarm is closer to a bias grain. What this means is that the side of the sleeve with the bias grain will easily stretch out, but the piece on the straight grain will not. If you do not pay attention when sewing you will end up with one side of the sleeve being longer than the other. I recommend to put pins in this seam and sew gently, easing the bias edge ONTO the straight edge. Do not stretch the straight grain to match the bias edge.
Overlock the edge of the seam from the cuff all the way to the centre front in one step.
Turn the shirt right side out again and it should now look something like this. You are now ready to topstitch the yoke/sleeve seam that runs across the body and down to the cuff. Topstitching here is optional, while it is a nice way to ensure the seam stays flat, it is mostly a design feature.
Make sure the seam allowance is pushed upwards towards the neck and away from the pocket. Start the topstitching at the centre front of the body, and continue along the length of the body until you get close to the armhole, drop the needle down so you can re-adjust the garment under the machine as shown in the next step.
When topstitching on top of a tube or a closed piece (like a sleeve) its very easy to accidentally stitch through the underneath layer. Bunch the sleeve up like a donut with a clear hole in the middle and that way you can keep checking the underneath is clear as you move along. Continue the row of topstitching you started at the centre front until you finish at the end of the sleeve.
Repeat the same processes for the other side of the body and sleeve and you should now have a garment which is ready for a button stand, collar and cuffs!