A coordinate system is a way of assigning a set of numbers to the a set of numbers so that each point has a distinct set of numbers. (That's a very general definition because you the concept of a coordinate system is very general.)
The simplest example is the number line: Choose some starting point on the line and call it "0". Choose some unit length to measure with. To every point on one side of "0", assign its distance from 0. To every point on the other sided of "0", assign the negative of its distance from 0.
Once you have that, it's easy to set up a coordinate system for the plane: Choose some point in the plane. Draw a two lines through it at right angles (right angles is not necessary but makes things much easier). Assign numbers to each point on the two lines as above, assigning 0 to the point where the lines intersect. From every point in the plane, drop a perpendicular to those lines. Assign to that point the pair of numbers on the lines where the perpendiculars cross them.
Same thing for three dimensional space except that now it is possible to have 3 perpendicular line through the same point so we get 3 numbers for each point.
As for "how to find angle b/w two connected lines", that depends upon how the lines are "given" as well as whether you are working in the plane or 3 dimensions.
If you are given equations for the lines in two dimensions, you can combine their slopes. If you are given parametric equations, you can form the unit vectors pointing in the direction of the lines and use the dot product.
[tex] tan (\alpha) = m [/tex], that's the only way I know to find the degree between angles in a two dimensional set of axes. M is the slope and [tex] \alpha [/tex] represents the angle between the line and the x axis. Not sure if this helps.