Dandelions are hard to kill as they have a deep taproot and they self-seed prolifically. If you have the time or if there are not too many dandelions, then digging them up by hand is very effective. Alternatively you could use a lawn weed killer which will specifically kill broad-leaved weeds such as dandelions but will have no effect on the grass. Specific lawn weed killers are available in all good garden centres. Once you have eliminated the weeds it is also worth giving your lawn a high nitrogen feed (Chempak® High Nitrogen Feed - Formula 2) in the spring to keep it in good health and vigour, reducing the risk of weeds taking a hold. The healthier the lawn, the less likely weed seeds will be able to germinate and grow.