How does decision tree for regression makes a prediction?
Depends on the implementation but commonly used is a certain cursive partitioning method called CART.  The algorithm works as following:  It searches for every distinct values for your predictors and chooses to the split based on what minimize the SSE for two groups of dependent variables.  The difference is within the SSE is usually the difference between the actual value and the average of the sample or the difference between the actual value and the output of a linear regression.  For each group, the method will recursively split the predictor values within the groups.  

In practice, the method stops when a certain sample size threshold is met.  The node with the lowest SSE becomes the root node.  

Reference: You can read more about tree based regressions here: Tree-based regressions