Hi MZET, welcome to PF.
The relation " Since speed = wavelength x frequency" is true for a given medium.
Frequency depends on the nature of the source. Speed and hence the wavelength depends on the nature of the medium.
So for a given medium, as frequency increases, wavelength decreases.
The speed of the wave is based on the properties of matter it travels through. I would recommend treating it as constant for a while.
Let's have a theoretical wave with frequency of 1Hz and travelling at 1m/s. What it's wavelength. Now what happens if you double or half the frequency?
If you understood that, you can send you wave through another matters where it travels with say 2 m/s or 0.5 m/s.
If all above done, start travelling yourself. Go 0.5 m/s against and with the 1 m/s wave. How often will you encounter the same phase (e.g. top) of the wave? This is Doppler effect.