Alappuzha (Alleppey) is about 50km (31miles) south of Kochi.
This is an hour's drive.
By road is the popular way to travel,though there are train connections between the two cities.
South bound trains travels either via Kottayam or Alleppey. Ask for the ones travels via Alleppey . Most of the Alleppey bound trains stops at Ernakulam Junction ( ERS), popularly called the South station. A few has stop at Ernakulam Town ( also called the North station).