Are there indicators for overfitting? Do high values of regression coefficients indicate automatically that there is an overfitting?
Is there a way to know when we are overfitting our data?
 A: No, specially as it depends on the scale of the input variables.
The indicative of overfitting is good performance in train set and bad generalization performance, meaning the learner "memorized" the train set, and this is assessed through resampling.
A: Yes, it is very simple.  Test your model on a Hold Out sample, a testing data set, or cross-validate it over numerous different Hold Out samples.  An overfit model is a model that fits the training sample very well but does not perform well over the various forms of Hold Out samples mentioned above.  If you are dealing with an econometrics model other indicators of models being overfit or badly specified include models that have a very high R Square (close to 1) and a very low Durbin Watson score (under 1.3 or so).  In such a case, your model has most probably a unit root in the dependent variable and in at least one of the independent variable (but your model is not cointegrate as your residuals are not stationary).  The easiest solution is to fully detrend all your variables.  Another indication of a model being overfit is when you have a really high R Square but some of your variables' coefficients are far away from being statistically significant.  In such a case, you have too many variables and you should eliminate the ones that have relatively weaker statistical significance.    
