A field is a commutative division ring. You can add, subtract, multiply, and divide in a field, and + and * are commutative and associative. Elements have inverses, and multiplication distributes over addition.
The concepts of characteristic, isomorphism, and subfield carry over from rings.
Every field contains the subfield generated by 1. This is either the rationals (characteristic 0), or the integers mod n (characteristic n). Actually we know that n is prime, for if a*b = n, then a and b are zero divisors, elements that are not invertible. Every field is based on Z or Zp, where p is prime.