Usually carries a negative connotation, implying a cunning, underhanded, or questionable way of doing something.
His way of doing things is always sneaky.
Don't fall for a scammer's tricks.
Standard spelling.
Rarely used kanji form.
Compound of やり (continuative form of やる 'to do') + 口 (くち 'mouth; way'). The negative nuance likely developed from the idea of a 'mouth' or 'opening' used in a cunning manner.