How to choose the order in which to split a decision tree?
One option is to use a simple approach, like just choosing random attributes, or taking one at a time. 

Another option is to use a metric to decide, at each step, the attribute that best splits the data. Different tree algorithms apply different metrics, like for instance Gini impurity (CART algorithm), or information gain (ID3 and C4.5 algorithms).

You can read a brief description of these methods in the "Decision tree learning" entry on the Wikipedia.