Once we have constructed a decision tree from the data with the attributes A1, ..., Am and the classes {c1, ..., ck}, we can use this decision tree to classify a new data item with the attributes A1, ..., Am into one of the classes {c1, ..., ck}.
Given a new data item that we would like to classify, we can think of each node including the root as a question for data sample: What value does that data sample for the selected attribute Ai have? Then based on the answer, we select the branch of a decision tree and move further to the next node. Then another question is answered about the data sample and another until the data sample reaches the leaf node. A leaf node has an associated one of the classes {c1, ..., ck} with it; for example, ci. Then the decision tree algorithm would classify the data sample into the class ci.