Essentially, pattern drafting is the act of making something two dimensional (the fabric) fit around something three dimensional (the body). Darts are a way of doing this and are most commonly used to create shape around areas of the body that are curved - the bust, shoulders, elbows and waist, but can be used pretty much anywhere - whether purely for fit, or also as a design detail.
You may have put a dart in something before and noticed that the dart has changed the shape of the seam that it lies on and is no longer the smooth line it once was.
In the image above a dart has been added to the armhole and has drastically changed the shape of the armhole, preventing it from being able to fit with the sleeve pattern.
To prevent this from happening, you need to add dart shaping. This will ensure that once your dart is sewn your armhole (or which ever seam your dart is located) will remain a smooth line (like the dotted line).
Trace your patter onto some pattern paper without seam allowance, ensuring you have extra paper around the dart to make the changes (in this case, around the armhole).
Think about which direction the fullness of your dart will be pressed once it is sewn, this will decide which dart arm you need to fold.
In this example, I chose to press the fullness up towards the shoulder, so will focus on the upper dart arm.
Generally vertical darts are pressed towards the centre front (in the case of front darts) and the centre back (in the case of back darts). It seems reviews can be mixed when it comes to more horizontal darts, but after looking at this post I was convinced to push mine up.
Fold along the dart arm to the point of the dart.
Working with darts on a flat surface can be difficult so move over to the corner of your table (hopefully you have a square or rectangular table like me, otherwise a big book will do the trick), placing the point of your dart on top of the corner of the table. You quickly see that it is much easier to get the dart to sit flat once it is on the corner.
You will see that your seam (in this case the armhole) has become disconnected.
Take some sort of weight to keep your pattern in place on the corner (in my case my very handy, well used and trusty can of soup) while we redraw the armhole.
Redraw the armhole (I tend to use a different coloured pen so as not to get confused by my lines) by drawing a line between the disconnected seams. Make sure your line eases gradually back into the original seam at either end.
Take your tracing wheel and trace along your new seam line - particularly focusing on where the dart is folded (go over this area a couple of times to ensure the markings have come through).
Unfold the dart. You will see the markings transferred from the tracing wheel.
Take a ruler and join the dots to form a straight line.
Repeat for both sides of the point.
At this point it is finished and you can just add seam allowance and get sewing.
I cut out my armhole to show that now when the dart is folded the armhole seam sits flush at the seam.
And as you can see by the indents on my table, this corner has seen a lot of darts!