A reaction rate is expressed in terms of moles per liter per unit of time (usually seconds, but may be something smaller like picoseconds or even femtoseconds for particularly Speedy Gonzalez-esque reactions). This is the same as saying molar per unit of time. Because of the inverse relationship between the decrease of reactants and the increase of products, reaction rates are written in an equivalent relationship which takes into account their molar values. For a typical reaction,
aA + bB --> cC
... the individual rates of decrease/increase of each reactant/product are written in a ratio,
... where t represents time. When put into the context of the broader chemical reaction, proportions of moles must be taken into account, as well as whether the reactant is increasing or decreasing. By dividing each concentration change by its coefficient in the balanced equation and making it negative to counteract decreases in concentration, all the rates of reaction can be made equal.
-1   ΔA       -1   ΔB        1   ΔC
-- * --   =   -- * --   =   -- * --
a    Δt       b    Δt       c    Δt
These equivalencies only express the average rates of reaction over a given period of time, to find the precise rate of reaction at a given moment one must take the derivative of the concentration change.

Reactions rates can be measured only by observing the change in physical properties linked to concentration over a period of time. The ways in which this is done are various, but two common methods include direct measurement through titration and spectroscopy, in which the changes of light wavelength as a beam is passed through a reaction indicate reaction rate.

Whitten, Kenneth W., Raymond, Davis E., Peck, Larry M. General Chemistry, 6th ed. South Melbourne: 2000.
Lecture notes

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