Often, a smooth response to a hormone means that some processes must be sped up and others must be slowed down.
How can a single hormone have opposite effects like this?
An hormone is not different from most other molecules. To have an effect on a cell it binds to a (more or less specific) receptor, located either on the plasma membrane or inside the cell, and it initiates an intracellular cascade of events1.
There are several ways an hormone can have different effects:
there can be multiple receptors for the same hormone. For instance, prolactin can bind to two receptors, called prolactin receptor (PRL-R) short and long form. The short form of the receptor has been shown to lack the ability to promote milk protein genes transcription (See Lesueur et al., PNAS - 1991).
the same receptor can be coupled to different intracellular pathways in different cell types / physiological conditions, thus resulting in different effects.
each cell type/tissue expresses a set of protein that will interact in a different manner with the intracellular cascade promoted by the hormone.
an hormone can interact with receptors for other molecules. For instance allopregnanolone, a metabolite of progesterone, is a potent agonist of the GABA-A receptor, giving it anxiolitic properties.
An interesting example is that of estrogenic compound. Several receptors exist for estradiol (E2). The "classical" receptors are called ER-alpha and ER-beta, and they are located in the cytoplasm. The binding of E2 to the ER promotes their dimerization and entrance into the nucleus where they can promote the transcription of various genes. ERs can also bind to other transcription factors and modulate their activity. So, depending on which transcription factors are present different genes will be transcribed in response to E2. Moreover, ER-beta can have opposite effects then ER-alpha (see for instance Weihua et al., PNAS - 2000). In addition, receptors like ERs can be activated also in absence of the endogenous hormone: for instance, dietary amino acids activate ER-alpha in liver by a mTOR-dependent phosphorylation (Della Torre et al., Cell Metabolism 2011)
To make things more complicated, membrane receptor for estrogen have been described, such as GPR30 (Revankar et al., Science - 2005), membrane "versions" of the classical ERs, plus various splicing variants of the ERs (mostly expressed in tumoral tissue).
GPR30 in breasts has been shown to activate certain molecular pathways (notably Erk1/2) that contribute to cellular growth (Filardo et al., Mol Endocrinol. - 2000), possibly linking it to proliferation of ER-negative breast tumours. Other tissues that do not express GPR30 will lack this E2-induced proliferative stimulus.
So, tissue- or time- dependent modulation of the receptors and of the intracellular pathways associated with it can allow the body to respond to the same hormone (or, more in general, to the same molecule) in opposite ways.
1 This is a simplification, not every substance (and not every hormone) acts by binding to receptors, but let's keep things simple.