Step 1: Identify what kind of sugar lactose is.
Lactose, the sugar found in milk, is a disaccharide, meaning one molecule of it is actually built from two simple sugar units joined together.
Step 2: Identify the two units and how they are joined.
The two units are D-galactose and D-glucose, connected through a $\beta$-1,4-glycosidic bond running between carbon 1 of galactose and carbon 4 of glucose.
Step 3: Break that bond with water.
Hydrolysis, carried out by dilute acid or by the enzyme lactase, adds a water molecule across the glycosidic linkage and splits it apart: \[ C_{12}H_{22}O_{11} + H_2O \rightarrow C_6H_{12}O_6 + C_6H_{12}O_6 \]
Step 4: State the two products.
The reaction releases one molecule each of galactose and glucose in equal amounts. \[ \boxed{\text{Galactose and Glucose}} \]