Regarding first (and second) question: A general approach to reduce misclassifications error by iteratively training models and reweighting rows (based on classification error) is Boosting. I think you might find that technique interesting.
Regarding second question: The question sounds a little bit naive to me (but I maybe did not understand your true intention), since reducing misclassification error = improving model performance is one of the challenges in Data Mining / Machine Learning. So if there were a general all-time working strategy, we all would have been replaced by machines (earlier than we will anyways). So I think that yes, the general approach here is educated trial and error. I suggest this question, Better Classification of default in logistic regression, which may give you some ideas for both questioning and model improvement.
I suggest to play around a little bit and then come back to ask more specific questions. General questions regarding model improvement are hard to answer without data and/or additional information of the circumstances. Good luck !