Is dermatitis very contagious?

Depends on cause. Eczema or dermatitis are general terms we use to describe a group of inflammed skin conditions that causes chronic, itchy rashes. Types of eczema include: allergic, contact, irritant, nummular eczema, and many others. For the most part, these are not contagious but rather may involve a person's overactive immune system in the presence of certain conditions, materials or allergens.
Depends on what kind. Depends on what kind of dermatitis. That's a very nonspecific term for any rash of the skin. Sone rashes are infectious in nature such as tinea corporis (ringworm) or impetigo (staph infection).