Andrew,
I wanted to add some information to Sandra's answer.
There are different methods to measure current, some are intrusive and some are not. The method used by most DMMs is using a shunt (commonly a resistor with a value in the mOhms range and with a relatively high power rating, among other characteristics) that connects in series with your circuit, hence it is an intrusive method (unlike the magnetic probes), however it is accurate so it is widely used. When the DMM is calibrated the value of the shunt is measured. This allows the DMM to measure the voltage drop across the shunt and calculate the current using ohms law.
You could use the same method to do your own measurement. However, be aware of the errors you could be introducing and make sure you protect your shunt. The accuracy of your measurement will be better if you use the built-in shunt of the DMM (the actual current ranges of the DMM), but sometimes you do need to take higher current measurement and resort to an external shunt.
Considerations about protection:
Notice, for example, that the CSM-10A is a fused shunt, so in reality you have a fuse in series with the shunt and then your DMM is measuring the voltage drop across the shunt only. But the fuse is there to make sure your shunt does not blow if you happen to connect more than the rated power of the shunt. Then you can replace the fuse (wich can be found in RadioShack or Fry's) and continue taking measurements.
Considerations about measurement errors:
If you build your own shunt, make sure you do a Kelvin connection. This is, make sure that you are measuring the voltage drop across the shunt at the shunt terminals directly.
Also make sure that your DMM is configured in the highest input impedance possible for the range you are using. This will make all the current to flow through the shunt only and not get divided through any parallel impedance at the DMM terminals.
The value of the shunt is also important. You do not want it to be very big because it will load your circuit and you will not be doing a very accurate measurement. Check the NI Digital Multimeters Help file (https://www.ni.com/docs/en-US/bundle/ni-dmm/page/ni-dmm.html) for information on Burden Voltage and Resistor Self Heating.
Make sure the shunt you choose can withstand the maximum power you will be delivering to it.
Finally, be aware that the accuracy specifications of your measurement will depend on the accuracy specs of the DMM and the specifications of your shunt.
Shunt manufacturers usually post application notes about how to use their shunts in current measurement applications, and explain more about the specifications of each shunt (if it changes value with temperature, the temperature coefficient, the effects of aging, etc). I recommend you to do a webs search for "current measurement" or "current shunts" in Google.
