Here is what you need to know:
1.What is the motor voltage?
2.What is the motor starting current?
3.What is the motor running current?
Knowing that, we could pick a suitable relay. Is the one you show up to the task?
The relay you have chosen
https://datasheet.octopart.com/LU-5-R-Rayex-datasheet-10584258.pdf has a max contact current rating of 2A. Is that enough to switch the motor?
Presumably, you intend to write code to switch a port pin high/low to start and stop the motor? The UNO runs on 5V when powered with the USB, meaning that its port pin will be close to 0V when low, and close to 5V when high. The port pin can only deliver <40mA to an external load, per the limitations of the port pin circuitry inside the ATMEL chip. Is that enough to drive the relay coil?
According to the relay data sheet, the coil voltage requirement is nominally 5Vdc @ 40mA, so connecting the relay coil directly (without a transistor) to the port pin might just barely work. However, it would be marginal, because the ATMEL port pin will not simultaneously deliver 5.0V and 40mA. It will deliver 5.0V @ zero current, but might only deliver 3.5V @ 40ma, so putting a switching transistor between the port pin and the relay coil is a good idea.
Another thing to check: How much extra power can you expect to steal from either the 5Vout or the 3.3Vout pins on the UNO? You would have to read the UNO specs to find out. It may turn out that the relay coil should be powered from the external power supply that runs the motor; not from either the 3.3Vout or 5Vout pins on the UNO.
After you answer some of these basic questions, we can show how to hook up a transistor to switch the relay coil.
Note that you do not have the motor side of the relay wired correctly. Look at the pin out, below: