If you want to improve the look, feel and manageability of your hair, a conditioner is certainly a good idea, yes. Regular shampooing tends to strip hair of its natural protective oils and brushing, blow-drying, central heating and hostile weather can damage the hair’s outer surface.
Each hair is covered in tiny cells which look a bit like fish scales and damage to the hair causes these to stand out which makes the hair look dull and out of condition. Conditioners work by smoothing down these “cuticles” so your hair looks smooth and shiny again. They’re also great at reducing static.
All hair types benefit from conditioning but with greasy hair the trick is to use the conditioner sparingly and if hair is long, to concentrate on working it through the ends which tend to be drier.
As for how long you need to leave it on your hair, the answer is not long. You can usually ignore whatever it says on the bottle unless you’re using a ‘leave-in’ conditioner – most good ones work immediately so can be washed off once you’ve massaged them in.