This only works from within Speed Dial, not the Contacts application.
Edit or create a new Speed Dial entry. Give it a label, define a telephone number. Then tap the "More" button.
In the "Extra Digits" field, enter a comma ( , ) to give a one second pause, enter any numbers that need to be toned out to the voice menu system being dialed into, and you can enter a pound ( # ) character too if that's required by the voice menu.
Probably you want to check mark the "Dial Extra Digits authomatically" option too.
Tap OK and OK again. You're done. Now test it out.