Classless addressing allows for variable-length subnet masking, decoupling IP addresses from default subnet masks. It works by allowing arbitrary network masks to be assigned without respect to class. Addresses are notated as p.q.r.s/n, where p.q.r.s is the IP address and n is the mask bits. Classless addressing systems follow three rules - using contiguous IP addresses notated in CIDR block format, block sizes being powers of 2, and the block's first IP address being divisible by the block size. It provides advantages like more efficient IP address and routing table utilization.