Cloud forms because the airmass is forced to rise eg a wind arriving at ridge. As it rises it will cool at the dry adiabatic lapse rate. As it cools it will become less able to hold moisture becoming more & more humid.
If it continues to rise then eventually it's humidity will become 100%. Any further cooling will force water to condense out of that parcel of air. In other words cloud/fog will form.
While the rising parcel of air has less than 100% humidity it will cool at the 'dry adiabitic lapse rate' (DALR) ==> 3 deg C / 1000'.
If/when it gets to the point of condensation then any further cooling will be at the 'wet adiabitic lapse rate' (WALR) ==> 1.5 deg C / 1000'. The WALR is less than the DALR because the condensing moisture releases its 'latent heat of evaporation'.
Knowing the starting temperature & the dewpoint you can derive the cloudbase.
As the air rises it initially cools at the DALR until the dewpoint temp. is reached, then it cools at the WALR.
eg. Starting conditions: Sea level, 25 deg C, Dew point 13 deg C.
At first the airmass changes temp at DALR (3 deg C / 1000') so at 1000' its temp will be 22 deg C,
2000' == 19 deg,
3000' == 16 deg,
4000' == 13 deg Dew point: moisture condenses/cloud or fog forms. From here it cools at WALR.
5000' == 11.5 deg
6000' == 10 deg
Until the mechanism forcing it to rise stops.