What to do after training a classifier?
To see which attributes influence your model will depend on the type of model you are using. For Decision Trees, Random Forests, and Gradient Boosting based on trees you can plot feature importance metrics.

In linear models such as Logistic Regression, theoretically the coefficients will indicate how much the model will be influenced by their features.

Are you using Python? Let me know which models are you using so I can help you more.