This is the most basic SQL you could ever write. It's called an inner join, where you join two tables together by using a value common to both, in this case, the depID. As you have two tables, you need to join twice, as in
select E.EmpID, E.Emp_Name, d1.DepartmentName, d2.DepartmentName from Employee e inner join department d1 on e.DepID1 = d1.DepID inner join department d2 on e.depID2 = d2.DepID
You should buy a basic SQL book and read it.