SetDirectory[NotebookDirectory[]]; list = {{3, 4, 5}, {4, 5, 6}}; Export["data.txt", list]
To read it later, say after closing and restarting Mathematica again to continue working on the data
SetDirectory[NotebookDirectory[]]; list = ToExpression@Import["data.txt", "List"] {{3, 4, 5}, {4, 5, 6}}