The ecliptic plane is the plane of the Earth's orbit around the Sun. The equatorial plane is the plane of the Earth's equator. The Earth's equator is tilted at an angle to the ecliptic plane. The intersection of those two planes forms a line. This line forms the x-axis of the geocentric equatorial plane.
This line also runs through the center of the Earth, which is the origin of the geocentric equatorial coordinate system. The only thing left to do with this line is decide which direction is positive and which direction is negative. Twice a year (vernal equinox & autumnal equinox), the line formed by the intersection of the ecliptic plane and equatorial plane runs through both the center of the Earth and the center of the Sun. The positive direction for the x-axis runs from the center of the Earth to the center of the Sun on the vernal equinox.
Right ascension measures the position of the star relative to the positive x-axis (the direction of the vernal equinox) around the equatorial plane. You use the right hand screw rule to figure out which direction is positive (positive would be counter-clockwise if viewed from the outside of the system).
And, yes, many astronomical books identify right ascension, which is an angle, by Hour Angle. There's approximately 15 degrees per hour (15.04 if you want to be a little more exact).
Declination measures the North-South position of the star relative to the equator. Positive angles are to the North. Negative angles are to the South.
As someone else mentioned, the long term position of the stars isn't stationary due to precession of the Earth's axis, which leads to a somewhat strange situation. If it doesn't happen to be the vernal equinox, you need a different method to find the positive direction of the x-axis. The solution is to look at the star (or a point in space relative to a few stars) that would be directly behind the Sun on the vernal equinox. This star (or point in space) is called the First Point of Aries. You'd think this point must lie in the constellation Aries, but, thanks to precession, the First Point of Aries actually lies in the constellation Pisces (it's too hard to go back and change books already printed so the term has never been changed even though the point has moved).
Someday soon (at least in astronomical terms) the First Point of Aries will enter the constellation Aquarius. And, at that time, there will be much singing.
