I am trying to power a small peristaltic pump using an UNO R3. I have it powered using usb, and I tried running the blink program to see if I could power it using digital write, and extended the delay to troubleshoot voltages using a multimeter. The motor doesn't do anything connected to the digital pins even when the digital write is set to high. If I connect the motor to the 5 V power pin the motor turns on so I know 5 V is enough voltage. I've looked at tutorials for DC motors and they explain how to set it up with motor reversing using components I don't have, and I don't need it to reverse. How can I get the motor to turn for a specific length of time?
Most likely the motor you are trying to drive requires much higher current than what the UNO can provide through its digital outputs.
Check out this summary to find out detailed specs for the I/O ports.
What you could do is to draw power from the 5V line provided by the Arduino. If that can drive your motor, then use the line to power an output stage, driven by the digital I/O. See this example. In general, the idea is that the digital I/O provides the control logic, while the output stage provides the power required by the specific load.
The typical loads that can be driven directly by GPIOs are low power LEDs. Anything that involves moving parts is generally out of reach, power-wise.