How do I power an arduino without USB?
my arduino talks to another device that uses serial communication


What other device? You haven't said which Arduino, but Arduinos are generally "devices" which talk to a "controller" (host) which is generally a PC / Mac.

The host has the job of supplying power (via the USB cable) to the device. Thus your Arduino will be powered by the device it is plugged into.

Disregarding this issue for the moment, you can supply regulated 5V power directly to the 5V pin on the Arduino. On the Uno (and many others) this is labelled "5V".

The power jack is to supply 7V to 12V (eg. from a wall-wart) which then goes through the voltage regulator on the Arduino (depending on the model in question).

There is quite a discussion about this on https://www.arduino.cc/en/main/arduinoBoardUno. On that it mentions:


  Supplying voltage via the 5V or 3.3V pins bypasses the regulator, and can damage your board. We don't advise it.


This is true. Directly supplying 5V to the 5V pin bypasses the regulator and also bypasses the reverse-voltage protection diode. However it is possible to do it.




  What about the Vin pin?


For a Uno you can see from the reference schematic what happens:



The power jack (on the left) goes into the reverse-voltage protection diode (D1). The other side of that becomes Vin. Then it goes into the 5V voltage regulator (U1). The other side of that becomes the 5V line.

Thus to supply 5V you can provide 5V power to the pin marked 5V. It is probably not ideal, because the voltage regulator may not be designed to have power applied on its "output" side.

There is more circuitry to decide whether to use the USB power or the Vin power (not shown above).