If that is a mechanical relay, then the Arduino probably doesn't have enough output current on a digital pin to drive the coil of the relay. You need to buffer the output with a transistor. I recommend a BS170 (which is a MOSFET). The full circuit will look like
digital pin -> 220 Ohm resistor -> Gate of MOSFET
+5V -> relay coil -> Drain of MOSFET
Source of MOSFET -> GND
However, it looks from the Tinker relay that it actually contains this buffer already. If that is the case, then you should hook it up according to the "tinker" connection cabling, which I have no idea what it is. My guess is it might be:
Arduino -> Relay
+5V -> "+" pin
digital pin -> unlabeled
GND -> "-" pin
With correct hookups, the relay should light green when the Arduino has power, and yellow when it's actually activated, according to the description I found on Google.