Yukari has three fairly different stages at all game points.
Early game/laning phase=Denying, a character that either keeps the enemy hero farther away than the exp range of creeps or constantly denies own creeps. In Yukari's case, gapping them away. Yukari has it easy since on top of gapping, she can choose to deny further(Really giving the enemy slim pickings) or gather up gold of her own. She has high base damage and high int, so she can last hit well with the right starting items.
Mid game=Ganker/nuker. You get a nice little stockpile at this point and your teleport and gapping skill should be adequate enough for you to start moving around and sneaking behind people in their own lanes for easy kills.
Late game=pusher/support. By now Yukari's lack of damage is really noticeable, but her gapping skill is now such a fast cooldown you can stockpile enough creeps for a short fight, amass a small army for when you succeed, and gap away dangerous enemy heroes or saving ally heroes from a super skill(Omae doesn't even do damage if in gap). Dropping creeps also has a large range so use that to pester and weaken them.
... Actually this post gave me a very good idea on a Yukari item build, I'll have to test it sometime.
