今 ima is now; 笑い warai is the verb to laugh in the form that links to what follows; 後で ato de is afterward; 泣く naku is to cry, and it comes last because Japanese puts its verbs at the end, which for this motto is the right place for the crying. The English circulates with the paired masks of comedy and tragedy, a tattoo tradition with no author and no date that anyone has fixed.
Japanese has a saying about laughing and crying, 今泣いた烏がもう笑う, the crow that was crying a moment ago is already laughing, but it means a child's quick change of mood and runs the other way; this design's sentence is the house's plain Japanese for the English motto, and it says exactly what the English says.
We want you to be as happy with the meaning as you are with Master Takase's art. To learn more, visit Philology of 今笑い後で泣く.