Determining the right ascension of an object is no more difficult, although slightly less intuitive than declination. This time we measure not in degrees, minutes, and seconds; but rather in hours, arc minutes, and arc seconds along the celestial equator, in much the same way as we measure along the horizon to get an object's azimuth in the local coordinate system.
There is nothing magical about measuring in hours instead of degrees; all we're doing is dividing the circle into 24 big pieces instead of 360 smaller pieces. If you want to, you can think of one hour as 15 degrees, but since the sky rotates one hour of arc for every hour of Earth time, astronomers find it more useful to measure right ascension in hours.
Be careful to note, however, that one minute of declination and one arc minute are not the same. One minute is 1/60 of a degree but one arcminute is 1/60 of an hour, and an hour is equal to 15 degrees!