The exact number of couplings, t-connectors, etc. will vary from project to project. You'll determine what is needed at the hardware store.
In the plumbing aisle, start selecting the materials. Pipe comes in various dimensions. I used 1/4" black pipe. Choose your preference. For this project, it's a good idea to purchase extra materials whenever possible. They can always be returned later if they are not used.
Lay everything out on the aisle floor. Use a measuring tape, drawing or template to make this process move smoothly and help you visualize the pot rack. Lay the corner elbows out first and find the lengths of pipe that work best to create the sides. Tip: T-connectors are needed wherever a supporting pipe will go to the ceiling.
At least two unions (or couplings) are needed to attach one side of the pot rack to the other. They will prevent any problems with pipe thread running in opposite directions. Tip: Ask the assistant in the pipe department to review your plan. Their advice can be helpful.
Select the s-hooks. Bring a piece of your pipe with you to make sure the s-hook fits over the dimension of the pipe. You'll need one hook per pot/pan, approximately 3-4 hooks per side.
Consider the metal color of the s-hook. You can match or contrast the pipe metal. It's your choice.