There's an old wives tale that says, " ...vinegar for wasps and bicarb for bees ..." It's an easy way to remember that the sting from a bee is naturally acid, and that from a wasp is naturally alkaline. In the case of a beesting, the bicarb(onate of soda) neutralises the acidity of the sting. These methods deal with the after effects of the sting, but often leaves the poison in your system to continue working away.
At a recent MUBK Q&A forum, an Aspivenin Insect Poison Remover Kit was recommended. These are available HERE from Amazon. This is a small cylinder that creates a vacuum and will pull out the sting and the poison by sucking it out.
There is one thing to be aware of and that is the poison sacs on a sting. On the photo you can see how the poison sacs are at the top of the sting and if you were to try and remove the sting with tweezers, you would squeeze the sacs and deliver a full dose of poison that your body then needs to process! In fact on a fresh sting, you can see the poison sacs pulsing slightly as they pump the venom onto you, so best avoided if you can.
The quick way is to take a hive tool or blunt knife or flat object and slice the sting away. Whilst it leaves a minute portion in your skin, it removes the remainder of the poison sac and makes recovery much quicker.
Or use the vacuum method as described above.
After that an anti-inflammatory cream, anti histimine or cortisone cream will soothe the area and take away the irritation - in time.