1. Make an act of thanksgiving that you're not dealing with code written by someone trained in FORTRAN, where all variable names are two characters long and all function names are six characters long. "You can write FORTRAN in any language." If you do happen to be dealing with FORTRANesque code, give up now.
2. Become familiar with the idioms of every programming language, of every programming paradigm (structured, object-oriented, functional, event-driven, dataflow, etc.), and of every programmer educational background (high school/self-taught, CS degree, startup pressure cooker, etc.). If you don't have time to do that prior to starting on the current project, then let your attempt to reverse engineer the current project serve as a building block for the next time.