That very much depends on the water source. Some are quite constant, some are quite variable. Snow melt in the spring, application of salt to roads in winter, water utilities that buy from other utilities as demand requires, droughts, periods of heavy rain etc are the kinds of things that lead to variations. Required frequency of testing depends on how much the water varies and on what you are doing with it. If you are running it through an RO system it doesn't much matter that the source is varying. If, OTOH, you are lime softening, for example, it does.
Testing for the critical parameter, alkalinity, is very easy to do. Good kits can be had at modest cost from Hach and other suppliers. Most home brewers go an even cheaper route and use alkalinity test kits from aquarium suppliers. These are good enough. Same comments apply to hardness which is probably the second most important parameter. Unfortunately there are no simple tests for sodium and sulfate and chloride tests involve mercury salts.