Is it normal for your hands to be numb?

No, not normal. Numbness can occur from various reasons. Some potential causes include vitamin deficiency, nerve damage, nerve compression, alcohol over consumption, side effects of different medications, or as a result of different systemic medical conditions. Get evaluated by a professional to determine the exact cause of the neuropathy in order to obtain the best possible treatment.
Not normal. Your hand numbness may involve carpal tunnel syndrome, which may be due to keyboarding, repetitive flexion/extension activity, or occult metabolic problems.. Easily treated and reversed, so see a doctor and get this addressed.