The saturation vapor pressure curve in the figure above shows the relationship between parcel temperature $T$ and the saturation, or equilibrium, vapor pressure $e_s$. Most parcels have a temperature $T$ and vapor pressure $e$ that result in the parcel being "unsaturated." That is, the parcel's vapor pressure is lower than the pressure needed for the rate of condensation $R_c$ to match the rate of evaporation $R_e$ ($e < e_s \Rightarrow R_c < R_e $). In this case, we cannot "see" the moisture in the parcel - the parcel is not part of any dew or cloud formation.
The temperature for which the parcel's vapor pressure $e$ would be equal to the equilibrium vapor pressure $e_s$ is known as the dew point temperature $T_d$. The dotted lines on the figure show the direct connection between $e$ and dew point temperature $T_d$ for an air parcel, as well as the direct connection between parcel temperature $T$ and equilibrium vapor pressure $e_s$.
For dew or cloud formation, the vapor pressure $e$ of the parcel must be equal to its saturation vapor pressure $e_s$. (Actually, fog and cloud formation will begin for vapor pressure slightly less than $e_s.$) If the vapor pressure of a parcel is well below the requisite equilibrium vapor pressure, the temperature of the parcel must decrease to its dew point temperature $T_d$, the vapor pressure of the parcel must increase to $e_s$ by the addition of more vapor, or some combination of temperature decrease and vapor pressure increase must occur so that the vapor pressure is "close" to the equilibrium value.
Suppose a parcel has a temperature of 70 F and a vapor pressure of 15 mb. The dew point is the temperature the parcel needs to have for it to be saturated. We can use the saturation table to determine the parcel's dew point $T_d$. For a vapor pressure of 15 mb, the saturation temperature is approximately 55 F. Therefore, $T_d$ = 55 F.
Next, we can determine the relative humidity (RH) of the parcel. Recall the RH is given by $RH = 100 \times \frac{e}{e_s}$. We have $e = 15$ mb. Use the table to determine $e_s$ for 70 F : it is approximately 25.3 mb. Therefore, the RH is $100 \times \frac{15}{25.3} = 63.8\%$.
Suppose the temperature $T$ and $RH$ of a parcel are 75 and 50%, respectively. From this information, we can determine the parcel's dew point and vapor pressure. First, we use the RH formula to determine $e$ of the parcel.
$RH = 100 \times \frac{e}{e_s} \Rightarrow \frac{e}{e_s} = \frac{RH}{100} \Rightarrow e =\frac{RH}{100}\times e_s $
Use the table to determine $e_s$ for $T$ = 75 : $e_s$ = 30 mb. Therefore, $e = .5 \times 30 = 15$ mb. Next, find the temperature at which 15 mb is the $e_s$ : $T_d \approx 55$ F.