To instrument a board, the connection between the power supply and the target device needs to be broken, usually via a series resistor that's placed on the board. Sometimes the inductor needs to be lifted if no series resistor was included on the rail by the board's designer. In the ideal case, through-hole connections were also provided on the board for the connection of these off-board sensors.
Here are three close-up photos that show several boards that have been instrumented:
In all three cases, the sensors stand in place via the two outer current carrying wires. The middle and right used insulated wires where as the one on the left used bare wires. In all three cases, the sensor's + connection needs to go towards the power supply and the - connection goes to the target device. The outer wires here are 24-26 gauge. (The relatively heavy gauge wire is used to keep the series resistance of inserting a smart sensor to a minimum.)
The ground connection is the middle hole of the smart sensor. In the left and middle photos, a 30 gauge wire connects to the middle hole ground connection on the board. In the right photo, the ground wire was more conveniently added to a big cap just below the bottom of edge of the photo.
Here are wider angle view photos of two of the boards above:
The sensors on the left are free-standing since the current carrying wires are stiff enough to hold them upright. Care must be taken since too much flexing will cause a wire to break. Too much bending can also cause a short to the board (and that's why insulated wires were used on these boards). The board on the right has the sensors laying parallel to the board. They are not affixed to the board, but a wire is wrapped around the bundle of ribbon cables out of view past the right edge of the photo.
For boards without the through hole connections, the smart sensors need to be immobilized to keep from pulling the SMT pads off the board. If there is room on the board or sides of connectors or large components, the sensors may be attached down with foam double-sticky tape (see photo below, sensor affixed on top i.MX7ULP):
For boards where there are no convenient unpopulated areas or there are too many sensors, some other means needs to be devised to immoblize the smart sensors. In the left photo below, two inductors per sensor have been flipped and the two sensors inserted to instrument the two rails. The solder pads on the inductors would easily be broken off by any movement of the smart sensors, so a cage with clamps to hold the ribbon cables was 3D printed. On the back side, there is room for the aggregator to be zip tied to the bottom plate, so the instrumented board can be moved as a single unit with minimal flexing of the ribbon cables.
what is that purple colored board?
It's an external current sensor board: https://community.nxp.com/docs/DOC-335699