To "give way" means to allow something else to proceed without getting in its way (or without getting in its path). To "go ahead" is synonymous with "to proceed" (the implication of "proceed" being that you're moving forward, not backward). :D

Literalmente: In the last century steam trains gave way to electric trains. = En el siglo pasado los trenes de vapor dieron paso a los trenes eléctricos. Mejor inglés: In the last century steam trains were almost totally replaced by electric trains. Literalmente: The sale went ahead without any problems. La venta concluyó sin problemas. Mejor inglés: La venta concluyó sin problemas algunas.

"Give way," in that case, is something like "replace". So, in the last century steam was replaced by electric trains. "Went ahead", in that phrase means just that the sale was made without any problem, "went well". You can use "go ahead" to say that something could keep going, proceed, e.g: Go ahead, press the button. So, the sale "proceeded" without any problem.