The Magic Ring is a useful way to start shawls and hats
Decreasing on the forward pass
Tss2Tog is a common method for decreasing stitches on the forward pass. Insert your hook through behind the next two vertical bars, YO and pull up a loop.
Decreasing on the return pass
Decreases on the return pass are done by omitting a chain between stitches. On the next forward pass, all stitches decreased together are worked as a single stitch.
Increasing by working two stitches in one
For those times when a hole in the fabric is not ideal, carefully chosen stitches can be worked into the same stitch. This video shows a TMSS and TSS worked into the same stitch.