The Lanham Act is the primary statutory authority for registering a new trademark. 15 U.S.C. § 1051 et seq.

You can find a legislative history compilation on Proquest.

You can search for Lanham Act legislative history through Westlaw.

The Lanham Act provision containing all required steps for trademark registration can be found at 15 U.S.C. § 1051 under Subchapter I. The Principal Register.