how do hormones affect the metabolism of target tissues?

Answer 1

Different hormones do it differently. They mostly bind to a receptor on the target cell surface and then a variety of different effects occur.

Some hormones (such as Insulin) affect surface receptors (Insulin receptor) and send "second messengers" to various parts of the cell

Others such as Cortisol bind to a surface receptor and then penetrate into the cell nucleus to directly affect protein synthesis.