When comparing with the network output with desired output, if there is error the weight vector w(k) associated with the ith processing unit at the time instant k is corrected (adjusted) as
w(k+1) = w(k) + D[w(k)]
where, D[w(k)] is the change in the weight vector and will be explicitly given for various learning rules.
Perceptron Learning rule is given by:

w(k+1) = w(k) + eta*[ y(k) - sgn(w'(k)*x(k)) ]*x(k)