We have made measurements of the evanescent decay of the irreversible magnetization induced by magnetic cycling of solid superconducting cylinders in order to elucidate the mechanisms of Anderson's thermally activated flux-creep process. A superconducting quantum interferometer device coupled to the creep specimen by a superconducting flux transformer made possible observations of flux changes with a resolution of one part in ${10}^{9}$. The general applicability of Anderson's theory of flux creep was confirmed and the results were analyzed to show that: (1) The total flux in the specimen changed logarithmically in time, i.e., $\ensuremath{\Delta}\ensuremath{\varphi}\ensuremath{\propto}\frac{\mathrm{ln}t}{{t}_{0}}$. (2) The logarithmic creep rate $\frac{d\ensuremath{\varphi}}{d\mathrm{ln}t}$ is proportional to the critical current density ${J}_{c}$ and to the cube of the specimen radius. (3) The logarithmic creep rate appears to be only weakly temperature-dependent because a proportionality to $T$ is nearly compensated by the proportionality to ${J}_{c}$, which decreases as $T$ increases. (4) The creep process is a bulk process that is not surface-limited (in this case). (5) Flux enters and leaves the surface in discrete events containing from about one flux quantum up to at least ${10}^{3}$ flux quanta. (6) On departing from the critical state to a subcritical condition, the creep process tends to remain logarithmic in time, but the rate is decreased exponentially by decreasing $T$ and is decreased extremely rapidly by backing off of the applied field from the critical state. (7) At magnetic fields $H<{H}_{c1}$ on the initial magnetization curve, no flux creep was observed, but the logarithmic creep rate showed a modest increase above ${H}_{c1}$ and a broad rise as $H$ approached ${H}_{c2}$. The creep process is characterized by a dimension parameter $\mathrm{VX}$ consisting of a flux bundle volume $V$ and pinning length $X$, and by an energy ${U}_{0}$, both of which are supposed to be material-sensitive parameters characteristic of the irreversible processes. These parameters were determined from the experiments. Bundle volumes $V\ensuremath{\approx}{10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{3}$ and energies ${U}_{0}\ensuremath{\approx}1$ eV were found, indicating that groups of fluxoids must be pinned and must move cooperatively. The results are found compatible with a recent model for flux pinning that includes these cooperative effects.