A pencil! That is the total key! Use a pencil and go thru each square writing in the possible answers. Once you find what will not work in each square, erase or mark out those numbers. Whatever you have left is a process of deduction until you have the lone number in each square.
1. brute force method, that just places numbers sequentially in the first square, going the last know good number, then going until theri's another contradiction, then goes back again.