What will happen if a alkali spills on your hand?

If an alkali spills on your hand the first thing you'll notice is that your hands will get soapy, that's because the fats of the dead cells on the top of your skin are literaly turning into soap, if an alkaly penetrates further it can cause skin irritation(if diluted) or even dangerous permanent burns(if concentrated), that's due to the fact that strong bases react with a very large number of compounds on your skin, they usually are dehydrating agents and they often react exothermically with the water present in your skin. So you should quicky wash with water or with something more appropriate the interested area

Spilling alkali into your eyes, though, is far more dangerous, imagine when some soap goes into your eyes, it has got a pH of circa 8-9, it hurts a bit; now imagine to have a 1mol/L solution of NaOH(a commonly used alkali), it has got a pH of 14 so it's about 100000-1000000 times stronger than soap for your eyes(though this is a rough calculation, soap can contain irritants which aren't related to the pH). This would actually make look your eye like a cooked egg and you'll have a very high probability to lose your sight, if you wash it for enough time with water or vinegar(I know it's not that funny, it's an extreme solution) quickly you may have some chance to avoid serious damages to the cornea. This goes for non-toxic alkalis such as NaOH.

You should always wear protective goggles and gloves working with alkalis because they're really dangerous if misused.