I fully agree with Dr Ethan’s answer. The commonest cause if hand itch is hand eczema. Hand eczema can be aggravated by use of soap and detergents and contact with irritants so this should be minimized.
Sometimes, you may noticed tiny bubbles on your hands and this a form of hand eczema called dyshidrotic eczema.
Psoriasis and contact dermatitis are other possible causes.
The general measures for hand protection suggested by Dr Ethan are excellent. However, if the itch or rash is persistent, it is best to see your dermatologist or gp to get it assessed and treated.