Take a mobile telephone for emergencies, but remember that they sometimes don't pick up a signal at the foot of a cliff or in the remotest places.
Let someone responsible know where you are going, and when you expect to return.
Take a basic first aid kit with some plasters.
Wear safety goggles when hammering; and avoid hammering flint, which gives off dangerous tiny 'sparks'.
Always use a chisel and never hit a hammer with another hammer for the same reason. Dave Martill's former professor was blinded in one eye because he didn't follow this rule.
Take a high visibility vest, so that if you are out past your return time a search crew can find you.
Take a packed lunch plus some spare high-energy food and some drink.
Do not collect from overhanging rocks, and try to keep away from steep cliffs.
If you are working near cliffs, then wear a hard hat to protect you from small stones disturbed by the wind, birds or other animals.
Do not climb on cliffs unless you are equipped to do so and are experienced in rock climbing, and the cliffs are safe for such purposes.
Beware of mudslides or falling rocks during and after heavy rain.
Beware of getting trapped by incoming tides.
Wear good boots with ankle protection, and take some waterproof clothing.
Be careful not to strain your back if you find a fossil in a heavy rock.
And please do not try anything that John 'Mad Big Monster Digger' Howell does. Although he looks like a man obsessed abseiling down the cliffs in the programmes, in fact he has the back-up of the British Army and he is an expert rock climber. He makes its look easy and safe. In fact, it is extremely difficult and very dangerous, and most palaeontologists never abseil to find fossils if they can avoid it.