How should I wire toe kick lighting for bathroom vanity?
There's not a standard for this.

What I would do is:


Install a receptacle hidden inside the cabinet (depending on cabinet style, this could also be installed in the wall if there's no back on the cabinet, or you cut a hole)
Install a switch on the wall, that controls the receptacle
Install a second junction box in the cabinet for the low-voltage connection, and run a lamp wire (or similar low-voltage wire) from that down underneath the cabinet to the toe kick (leave it coming out of the top of the toekick to be connected to the LED strip. 
Plug in a transformer to the receptacle, and make the connection to the wire inside the second low-voltage junction box.


You could skip the junction box for low-voltage, but then you'd have to deal with the transformer being connected during construction, and think about how the transformer could be replaced if it ever broke (without having to tear out the cabinets).

The receptacle would also have to be GFCI-protected: so either it is a GFCI receptacle, or it is powered from the load side of another GFCI already in the bathroom. If you do this using an upstream GFCI, you could also run a 14/3 and wire the receptacle as split (so you have both constant and switched power).