Bearings to targets are designated from the point of view of the targeting ship, as opposed to where that target might be on a map. This makes sense if you consider that these vessels are probably moving at high speeds, and there may be no localized phenomena to reference other than themselves.
The system utilizes 24 �quadrants� around a central point, aligned along the ecliptic (if that is how the POV ship is aligned). The quadrants are assigned in a clockwise ascending order (most analogue reference instruments seen in the series, namely gimbals and dial faces on flight instruments, are arrayed clockwise, so it follows that this system is similar), with each assigned a designation using the Greek Alphabet.
Given the need to have a common reference point, the central point of the quadrant map is considered to be the reference point ship, which is probably always the Galactica. When the Galactica enters a new sector, she resets her navigational reference point to indicate point Alpha as some reference point in space to which her nose is precisely oriented. The 7.5 degrees of angle on either side of that point is considered Alpha Quadrant until such time as the Galactica performs another reset. The other 23 quadrants are then set in 15 degree arcs from there.
If the Galactica detects Cylon base stars in Delta Quadrant, this indicates that they are somewhere between 37 and 52 degrees clockwise of point Alpha. �Alpha Six� is just to the left of true point Alpha, whereas �Epsilon Seven Mark Four� is 59.5 degrees clockwise of point Alpha, and 4 degrees above the plane of the ecliptic.
Vectors are also given using this same system, but are stated as a vector off of the current line of travel rather than as a reference from point Alpha (�Delta Vector� is roughly 70 degrees to starboard, or just 70 degrees clockwise from the line of travel, while �Chi Vector� would be roughly 40 degrees to port, or 320 degrees clockwise from the line of travel).