How to set a minimum wage

How does a country set an optimum minimum wage, i have went through loads of website but none of them give me a satisfied answer. For example, median of a country's income, percentage of GDP and such seem too shallow and unfair as a medium of calculation.

What criteria define an optimum minimum wage? Is there even such a thing?

The reason why you haven't found a satisfactory answer is that there isn't one. There are several and depending on who you ask you will get a different answer.

Some people will say that the optimum minimum wage is 0 and that the state should note interfere in the matter. Laissez-faire.

Some people wants the minimum wage to cover basic living expenses. What that entails varies widely but is usually connected to the general economic level of the country. In some countries it covers only the cost of basic food for 1-2 people. In others it covers rent, utilities, food, a tv, a mobile phone.

Some people want the minimum wage to be as high as possible. Some unions.

Klas is right in saying that there is no neat economic theory that allows you to calculate the optimum minimum wage. So here is how an economic analyst might guide the process of a country setting a new minimum wage:

1. Pick a range of possible minimum wages to analyse, perhaps based on cost of living estimates, 90th centile wages, union demands, benefit payments, previous minimum wages, etc.
2. For each possible minimum wage, attempt to model the likely impacts on (a) the wellbeing of people affected by wage increases (e.g. decline in poverty), (b) the overall level of knock-on wage increases throughout the economy, and their effect on inflation and tax revenue, and (c) unemployment. Perhaps also expected rates of compliance and any enforcement costs (though enforcement is often minimal).
3. Present this information in an easily accessible way and offer politicians a choice of a few reasonable options. Unless you're talking about a small change (say, increasing the minimum wage 5%), a final decision is likely to be made by cabinet, based on the expected effect on the ruling party's electability.

That is how an analyst is likely to approach it; in reality, if the private sector and/or unions have a strong voice in government, the process might resemble more of a negotiation between two sides.