From personal experience, the sting from a European Wasp is more painful than a sting from a honey-bee. For most people, a painful reminder of the sting, sometimes lasting several days, is the only after-effect they will suffer.
Applying an ice-pack to the sting site helps reduce the pain and swelling. The ice-pack should contain a mixture of ice and water rather than placing ice directly on the skin.
Some sting victims may have a hypersensitive reaction, while others who have suffered several stings, may develop an allergic reaction. Allergic reactions to a sting may involve puffiness of the skin extending well beyond the sting site, or the development of an asthma-like condition making breathing difficult or, in severe cases, the heart may stop beating.
If a victim is suffering breathing difficulties, then a salbutamol inhaler ('Ventolin') should help breathing.
When a known wasp-allergic person is stung on a limb, the recommended first-aid treatment is the same as for snake bite, ie. the pressure-immobilisation technique.
The limb is kept still while a bandage is wound around the sting site. Wrap the bandage around the limb a few time away from the heart side of the sting (ie. towards the fingers or toes), then firmly wrap as much of the limb as possible bandaging upwards to the groin or shoulder.
The wrapping pressure should be firm but not constrictive. Seek medical attention as soon as possible.
Never apply a tourniquet.