To measure voltage on an electronic circuit, you don't have to insert the meter into the circuit. Instead, all you have to do is touch the leads of the multimeter to any two points in the circuit. When you do, the multimeter displays the voltage that exists between those two points.
For example, you can insert a voltmeter into the LED circuit so that you can measure voltage. In this case, the voltage is measured across the battery. It should read in the vicinity of 8.3 V. (9 V batteries rarely provide a full 9 V.)
To measure voltages in the LED circuit, spin the multimeter dial to a range whose maximum is at least 10 V. Now just touch the leads to different spots in the circuit. To measure the voltage across the entire circuit, touch the black lead to the LED lead that's inserted into the negative bus strip, and touch the red lead to the resistor lead that's inserted into the positive bus strip.
Here's an interesting exercise. Write down the following three voltage measurements:
Across the battery: Connect the red meter lead to the resistor lead that's inserted into the positive bus strip and the black meter lead to the LED lead that's inserted into the negative bus strip.
Across the resistor: Connect the red meter lead to the resistor lead that's inserted into the positive bus and the black meter lead to the other resistor lead.
Across the LED: Connect the black meter lead to the LED lead that's inserted into the negative bus and the red meter lead to the other LED lead.
What do you notice about these three measurements?