I want to make sure I don't ruin my circuit.
To find the exact current, do I measure it by putting my meter in between the positive lead and the switch?
You need to place your meter (in current mode) between the battery and the device, usually on the non-ground side, which is usually the positive side.
Note that in current mode, your multimeter will essentially (**) connect the two leads in a "dead short". Do NOT place them on both terminals of a power source (like the battery).
You multimeter will be operating as a "wire" which happens to show the current flowing through it.
(**) Worth knowing: There is some "stuff" between the two leads:
Any multimeter will have a "current shunt" connecting the two leads. This is a low value resistor over which the meter can measure the voltage drop to determine the current. The size of this shunt will change for various current measurement ranges of your DMM. It can be damaged by too much current!
A decent multimeter will also have a fuse in series with the shunt which will blow (hopefully) before damage occurs.
In a good multimeter this fuse will be a relatively expensive / harder-to-find high voltage certified fuse.
Why am I telling you this:
If you try and measure a current on two low a current range, you may blow the fuse and/or damage the shunt.
To avoid this, when measuring a current in which you are uncertain of the correct range, start first with the highest range (highest current) that your multimeter has, and then once you know approximately how much current is flowing, you can measure again on a lower range to get a more precise result.
eg: If I start on a 10A range, and see that the circuit is drawing < 0.5A, I might then measure in the 500ma range to get a better picture.
This a lot better than starting in the 500ma range and discovering that your circuit is drawing 5A (pop goes the fuse).
Dave