When an electron absorbs a photon, it gains all of the photon's energy at once. If this energy is more than the work function of the metal, then the electron is ejected from the surface, and any excess energy goes into its kinetic energy. This means that, once the threshold frequency is surpassed, raising the frequency of the photons further leads to more energetic - faster - photoelectrons.
Increasing the intensity of light illuminating a surface means increasing the number of photons being delivered to that surface per unit time per unit area. This will result in more photon-electron interactions per second, and, consequently, more photoelectrons being emitted in a given time. The intensity does not affect the energy of the photons, so the speed of the photoelectrons remains unchanged.