Equip ANYTHING that will make you sneak better. You’re also going to need to be handy with a lockpick. Obviously if the item is in some public place you can scout it out, but oftentimes the best time to grab something is either when the residents just plain aren’t looking (or aren’t home) or when everyone is asleep! Be sure to save and then use your best judgement on which course to take and nab the item!
Return to Vex once you have the item for your cut ( 400 Gold ) and the job will be completed.