How to improve an existing (trained) classifier? I have a Classifier which I have trained and tested on a small dataset - receiving solid results, though I wish to improve them. If I understand correctly one way of doing so is to add more data to obtain a more precise classification rule. 

When doing this should I add data to both the training set and the test set? or should I add only to the training set? or maybe I should I create new training and test sets from the 'new dataset'? (new = the old data + the new data).
In order to improve your classifier, you have few options.


Ensembling - make a group of classifier and let them predict together. Stacking, blending, bagging, boosting. Choice is yours.
Hyper parameter tunning - you did not mention your tool, but i suppose that in every solid one is option to search in parameter space to find the best combination
Sampling - you can try undersample or create new samples (SMOTE) to give your classifier more data of class which you'd like to predict
Feature engineering - get rig of noisy features and work only with those which have an effect on your prediction, consider PCA too
Scaling - normalize your data can improve the performance, some classifiers require this
Data quality - missing values, coding categorical variables or suspicious values can influence performance