Stinging nettles are famously difficult to deal with – I mean, they are named stinging nettles for a reason: those nettles don't just scratch, they truly sting. Luckily, they are easy to tame with a quick dip in boiling water.
Bring a large pot of water to a boil and add at least a tablespoon of salt (this will help the nettles retain their crazily deep green color) before dumping a big tangle of nettles into the mix and stirring them down. Lift nettles out of the water as soon as they wilt, about 30 seconds or so, drain them, dunk or rinse them in cold water, and squeeze the dry by the handful (I find that first handful a bit difficult to grab – can they really be de-stung so quickly? yes they can!). Repeat with remaining nettles, if necessary.
Blanching nettles this way makes them easier to handle and store, and also makes it easier to clean them if the bunch you have is gritty (continue rinsing and draining until the water runs clear for particularly gritty nettles).