The best place to actually find fossils easily is The West Dorset section of the Jurassic Coast. Here the rocks are rich in fossils, and the frequent erosion of the cliffs by stormy weather, is continually exposing new layers of rock. Because the fossils would be lost forever into the sea, you are allowed to collect them from the beaches between Lyme Regis and Burton Bradstock. You are asked to follow a Code of Conduct to ensure the World Heritage Site is protected.
Try the beach below Black Ven Mudslide, between Charmouth and Lyme Regis. The dark patches of sand tend to be the places where fossils such as ammonites, belemnites, shells and bones can be found. Get onto the beach at Charmouth, which also has a Heritage Coast Centre with fossil displays. The Wardens there can provide advice and they also lead a number of fossil hunting walks.
In addition several guides work from Lyme Regis and can show you how to find fossils. Access to Black Ven from Lyme Regis is more dangerous than approaching it from Charmouth as you can be cut off by the tide along the way. On the western side of Lyme Regis you will find Monmouth Beach which has huge ammonites lying on the beach. These are far too large to remove, and you will only damage them if you try to move them. But you can get good photographs.
Devon & Dorset Coast World Heritage Site