I connected HC-SR04 ultrasonic sensor, to single-board computer BeagleBoard-xM. Trigger pin requires 5 V DC. However, control pins of BeagleBoard-xM can provide only 1.8 V DC.
What is the best way to convert voltage to 5 V? Is there anything else I should pay attention to?
First of all, according to the datasheet for the HC-SR04 that you linked to, it appears to run on 5v, not 3.3v.
What you need is a level shifter, to convert the I/O signals on the BeagleBoard-xM expansion header from 1.8v to the 5v levels (and back again) as required by the sensor.
A device that will perform this function is the Logic Level Converter from SparkFun. It has 4 channels, which is more than you need. You could build your own with just two channels, but for the price ($3) its not worth it.