Calculation of costs of goods manufactured and sold

A fairly open-ended question.

The costs that go into production are direct materials, direct labor and overhead. They go into the WIP while production is going on. Once something (or a batch of somethings) is finished, the total costs for that something are moved out of the WIP and into Finished Goods -- that's your costs of goods manufactured. In other words, it's still those 3 different costs, but only those of the goods that are already manufactured (past tense - finished).

The cost of goods sold is those very same costs, but it's the costs for those items which have been sold.

How you go about actually gathering up and calculating all these costs depends upon what kind of information you have and there is not "one" answer to that.