You are correct that generations are the relevant unit of time when considering evolutionary change. For example, mutation rates are generally measured in terms of mutations per generation. This occurs, of course, because the gene pool of a population cannot change until the current generation breeds and passes on a subset of its genes to the next generation.
As for how long a generation is, it is the age until reproduction. So, for humans this is on the order of 20 years (rather than human lifespan, which is a larger period of time). For studies of evolution in microorganisms (such as bacteria), we usually use the doubling time of the culture as the length of one generation. Note that the length of one generation can change over time (for example, as a culture of bacteria adapts to its environment its doubling time will decrease as replication becomes more efficient).