General method to make circuits?
Both suggestions in the comments in the OP were excellent and I agree with the users who provided them.  I have included these comments below for continuity:

There is en.wikipedia.org/wiki/Logic_synthesis but the general way of solving exercises in university is by understanding the material or asking your TAs if you have problems. – adrianN

Work with your peers. Students manage to pass the class somehow, so there must be a principled way. The course is designed to impart the mode of thinking which enables you to solve such exercises, but unfortunately the only way to accomplish this is by actually solving the exercises, on your own or together with friends. – Yuval Filmus 

To assist you, look at the Wikipedia pages here and here on digital circuits/adders.

Also, ask your instructor and/or TA for suggestions on a good computer architecture and design book.