Stinging / burning nettles are not a fun thing to grab hold of as you are doing a quick weeding of your potted plants or backyard garden. However, should you do such a crazy thing, there are two (really 4) actions you can take quickly.

1. Grab some tape and gently lay it across the hand and pull it off. You may want to do this multiple times. This will remove many of those miniscule spines. Those that are left behind are going to sting/burn like the dickens.
2. Make a paste of baking soda and slather your hand with it. This will balance the ph in the acid those little spines are releasing. It helps but sometimes the only thing you can do after that is live through it.
3. I took ibuprofen and benadryl later on because my hand actually blistered up a little and felt like the tingles when it has fallen asleep and is waking up – not sure how much it helped, but at least I felt I was doing something. The ibuprofen helped with the headache from clenching my teeth in pain.
4. Go get a treat for yourself and try not to cry too much. Yeah – it can hurt that much. Mine was a peppermint mocha from Starbucks.

For more information:

Wikihow – Treatments

Info from Univ. of California