To what pins of the relay do I need to connect a device to be able to control that device ? NO or NC? Why?
Normally Open (NO) and Normally Closed (NC) work as follows.

When there is no power applied to the relay coil, the Common (C, or COM) is connected to NC. "Normally", in relay land, means "when the coil is not being driven". When you apply voltage to the module input, the relay will be activated. At this time, COM will disconnect from NC and connect to NO.

You can see for yourself. Take your DMM and set it on "Ohms". Set it on the lowest setting, probably "200 ohms". 

Now connect 5 volts DC to the input at upper right on your photo. Connect the + to "VCC" and the - to "GND". Also connect the "IN1" pin to "GND". Leave "IN2" disconnected.

Now take your meter and connect to the upper 3 pins on the left side. Starting from the top, they are NO, COM, and NC. See the little graphic to the left of the terminals? The diagonal represents a switching arm which rotates from 45 degrees down to 45 degrees up when power is applied. And no, it doesn't do that inside the relay, it's just a convention to show how the connection is made. So, with no power applied (Normal), the center connects to the lower terminal, and the upper terminal is not connected. 

Check between NO and COM. You should see an overload on your meter, probably a flashing "199" or something similar. At any rate, it will be whatever you see when there is nothing attached. This is generally called "open", shorthand for "open circuit".  Now check between NC and COM. You should see something like 1 ohm or less (it will depend on your test leads and DMM). This is generally called "short" or "shorted", shorthand for "short circuit".

Now connect IN2 to VCC. You may well hear a slight click, and this is a good thing.

Looking at the outputs, NO and COM should show a short, and NC to COM should show open.

How you "connect something to be able to control it" depends on exactly what you want to do. 

For instance, if you want to drive a 5-volt lamp or LED, you can ground the - lead of the lamp/LED, and connect +5 to COM. Now you have a choice. If you connect NO to the lamp/LED +, the LED will turn on when you connect 5V to IN2, and turn off when you don't. On the other hand, if you connect NC to the LED, it will be on until you drive the relay, and will then go off.

If you have a 12-volt lamp, you can use a 12-volt power supply, and connect it to COM as above. However, you must continue to use 5 volts on the VCC and IN2 inputs. When you get more comfortable with the subject, you can use 12 volts on IN2, but you'll need a separate resistor, and you can ask a question about that, but that will be for another time.