If you have not done so, read the
Hardware Construction Survival Guide.
Read
Chapter 1. Implement the chips in the order presented starting at section 1.2.2 (page 19).
Implement and test Not chip using only Nand in the PARTS section.
Implement and test And chip using Nand and Not.
Implement and test OR chip using combination of Nand, Not and And.
Etc.
Hint for Or chip -- read about De Morgan's laws.
--Mark