using LOG in a econometric model I am a beginner at econometrics and I have to build a model explaining scholing (as dependent variable) by migration (independent variable) and a couple of covariables. I'm going to use fixed effects to do this.

Now my question is, where and why should I use a LOG? I already read a lot of questions and answers here but it didn't help me any further.

Should I log migration? Government expenditure on scholing? GDP/Capita? Literacy? Ratio of scholing?
The use of the natural $\log$ permits to obtain approximations of percentage changes instead of unit changes (assuming linear regression). For instance, the parameter associated with $\log$ of GDP per capita would give you the changes in education (in the unit you measured it, e.g., years) as a result of an increase of 1% in GDP per capita. Notice that if your dependent variable is also a $\log$ transformation, you'll obtain elasticities. 
To conclude, it should be straightforward for you to understand that there is no reason to apply a logarithm on unordered variables, or on binary variables. Its use on ordered variables is up to you, as the economic signification of choice of the estimates is dependent on your interests.