The Equatorial Coordinate System
The equatorial coordinate system is what astronomers use to keep track of the positions of objects in the sky. Astronomers imagine that the Earth is surrounded by a large sphere called the celestial sphereThis is a very large imaginary sphere around the Earth with the longitude and latitude lines from the Earth projected onto it.. The Earth’s equator and the plane of the Earth’s orbit are projected onto this sphere. 
The plane of the Earth’s orbit is called the ecliptic when it is projected onto the imaginary celestial sphere. Because the Earth’s axis of rotation is at a 23.5° to the plane of the Earth’s orbit, the celestial equator and the ecliptic are also at a 23.5° angle to each other. 
The plane of the ecliptic and the plane of the celestial equator intersect only twice a year, once on about March 21st of each year, and once on about September 22nd. The points on the celestial sphere where this occurs are called the vernal equinox (in March) and the autumnal equinox (in September).
For further information about the ecliptic, please consider watching the following videos:
The Relationship of the Celestial Equator and the Ecliptic
Celestial Coordinates:
To denote the positions of objects in the sky, astronomers use a system based on the celestial sphere. The use two measurements, right ascension and declination. Right ascension (abbreviated R.A.Right Ascension, abbreviated R.A., is a measure of distance on the celestial sphere measured eastward along the celestial equator. It is similar to longitude and is measured in hours, minutes and seconds.) is similar to longitude and is measured in hours, minutes and seconds eastward along the celestial equator. The distance around the celestial equator is equal to 24 hours.The right ascension of the vernal equinox is 0h 0m 0s.
Declination is similar to latitude and is measured in degrees, arcminutes and arcseconds, north or south of the celestial equator. Positive values for declination correspond to positions north of the equator, while negative values refer to positions south of the equator. The declination of the north celestial pole is 90° 0’ 0" and the south celestial pole’s declination is -90° 0’ 0". Declination at the equator is 0° 0’ 0".
The position of an object is stated with the right ascension first, then the declination. For example, the bright star Sirius’ position is R.A. 6h45m8.9s Decl. -16°42’52.1". The position of Betelgeuse is R.A. 5h55m10.3s Decl. +7°24’25.4".
While the equatorial coordinate system allows astronomers to describe the position of an object independent of position on Earth, the right ascension and declination of objects change slowly over time due to small changes in the Earth’s rotation over time due to a phenomenon called precession. So along with the R.A. and Decl. of an object, you will usually see the year or epoch those coordinates are valid for. The changes to the coordinates happen slowly enough that each epoch is 50 years long.
To Try:
Stellarium and Google Sky both tell you the coordinates of celestial objects. For practice you can try using one of the programs to find the following:
1. What are the coordinates of the star Rigel?
2. What are the coordinates of the star Vega?
3. What is located at R.A. 20h41m25.9s Decl. +45°16’49.2"
4. What is located at R.A. 5h16m41.4s Decl. +45°59’52.4"
Answers:
1. R.A. 5h14m32.3s Decl. -8°12’05.9"
2. R.A. 18h36m56.3s Decl. +38°47’01.9"
3. Deneb
4. Capella