There are three key advantages to using hall effect current sensors transducers:

They can be totally isolated from another high voltage electrical system which eliminate risk to delicate monitoring equipment and also minimizes safety concerns. In other words this sensor only detects the magnetic field around the wire, there is no electrical contact between the sensor and the wire. This is a nice advantage over using a current monitoring shunt precision resistor.
If your signal is too weak or you are not getting the resolution you want, you can simply loop the wire through the current clamp as many times as you want to double, triple, or quadruple the sensitivity or resolution of your sensor. For example, if your current signal is only .03 Amps, you could loop the wire through the sensor 10 times and the signal would by 10X stronger and would appear as 0.3 Amps.
Unlike the current shunt sense resistor which can have thermal temperature heat dissipation issues, the hall effect current sensor does not get hot. Even when measuring 70 Amps!

Example Wiring Diagram For the CLSA2CD Sensor Sold HERE on Amazon.com.

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The diagram above shows a 12 Volt DC wall adapter supplying voltage to a 8 Volt regulator. The 7808 Volt regulator puts out a very stable DC voltage. This is very important because the sensor outoput is only ~0.032 Volts per Amp that it measures, so if the voltage you are supplying the CLSA2CD is noisy, your data will get lost in the noise. The ground is shared through out the circuit. You could mount these components on a small piece of proto board like the one shown below. Or if you want to get one already assembled take a look at the one offered HERE

How to measure amps with a DMM Digital Multi Meter Volt Meter

STEP 1: Look up the owner's manual of your volt meter if you don't have one. Review the section on safety and measuring current.

STEP 2: Determine how many AMPs your digital multi-meter is able to measure before it blows it's fuse. (Most can handle about 10 Amps.)

STEP 3: Plug the black wire probe into the hole on your volt meter labeled "COM" or common or negative.

STEP 4: Plug the red probe into the hole on the DMM labeled 10A or + current.

STEP 5: Now disconnect the wire that you will be taking current measurements on.

STEP 6: Connect one wire from the DMM to the wire end using alligator clip patch cords.

STEP 7: Connect the other wire from your DMM to the terminal where your wire used to be connected.

STEP 8: Do not do this at high voltage unless you have had proper training. 12 Volts and under is typically pretty safe when it is under 10 Amps.

STEP 9: Turn on your DMM and then your circuit, you should see a number on your DMM indicating "Amps" If it is negative when it should be positive, then reverse the black and red cables on your DMM and that will fix the problem.