Hardness used without any modifier refers to the calcium and magnesium content of the water, or in hobby terms, the GH.
Alkalinity refers to the buffering ability of the water, or the carbonate/bicarbonate content of the water, or in hobby terms, the KH.
Nataku's suggestions for boosting each are usable, but I would suggest adding either or both to change water, never directly to the tank (asking for osmotic shock). And use GH and KH tests to monitor the changes.