The pH should not change more than 0,2 during 24 hours. If it is more, it can stress your fish.
The goal is to have a neutral pH of 7,0 for most fish, but this is very dependent on the type of fish you have. Some need alkaline water, other acidic water (so just about now is a good time to read about your fish and their needs).
The main reason for large swings in pH is a lack of minerals in the water - minerals in the water help keeping the pH more stable.
If the water is soft (lack of minerals) then it will have little buffer effect, so if you add a drop of acid to your water the pH will drop a lot. And the same: if you add a drop of an alkaline solution, the pH goes way up.
More information could be found in relevant articles on Wikipedia: one about soft water and one about pH scale.
By adding minerals to your water - mainly calcium and magnesium - you give the water a larger buffer capacity, so you will need a larger amount of acid/alkaline solution to change the pH up or down.
One reason for changes in pH during the night/day cycle is the photosyntesis stops at night, so the carbon dioxide is not removed. And it creates carbonic acid in the water and this makes the pH drop (low pH equals acidic and high pH equals alkaline).
So the normal swing in pH is less than 0,2 and this is within the normal range for most of the life we have in our fishtanks.
Be very careful when adjusting the pH in your water. Adjust it slowly and not more than 0,2 pH per day; this is to be sure your fish can adapt to the changes.
The content of minerals in water is often measured in German degrees of hardness GH or in parts per million; to convert degrees of hardness to ppm, you take GH and multiply it by 17,8.
A GH of 10-15 is good for most fish.