The speed of a wave is a property of the medium - changing the speed actually requires a change in the medium itself. If the medium does not change as a wave travels, the wave speed is constant.

Knowing the frequency and wavelength of a wave, it's easy to find the speed. In a time equal to 1 period, the wave travels 1 wavelength. The speed is simply the distance divided by the time, so:

v = λ / T

The frequency f = 1/T, so v = fλ

This makes it look like the speed is determined by the frequency and wavelength, but that is not the case. The speed is set by the medium itself.

A good example is a wave on a stretched string. For a string which has a tension T and a mass per unit length of μ), the wave speed is given by:

v = (T/μ)^½