step by step, how can the center of an earthquake be located?

Answer 1

I assume you mean the graphical method for finding an epicentre on a map.

1) Calculate the S-P time for each station. This is the time of the S-wave arrival minus the time of the P-wave arrival.

2) Take this time interval and a standardized graph of S and P wave distances. Find where the S and P waves are each of those time intervals apart. For example: If the S-P time was 3 minutes and each square on the S and P chart was 1 minute then find where the P and S curves are 3 squares apart. Read the distance from this point off the graph. This is the distance from the epicentre to each station.

3) These distances are the radii of the circles.

4) Draw a circle around each station the radius of the distance you calculated using the map scale on the map.

5) The intersection, or near intersection, of these circles is your epicentre.

Answer 2

One way to do it is called "triangulation". Let's say that you had three stations around the area of the earthquake; we'll call them Station 'A', 'B', and 'C'.
1) Station 'A' detects the earthquake's waves (rumbles) after, say, 15 seconds. Now, with a piece of paper, make a point, label it "A", and draw a circle with a radius of 15 units (centimeters, inches, etc.) around that point. The earthquake must have been on some point in this circle, because it traveled for 15 seconds from some direction before hitting Station A.
2) Now, Station B detected the earthquake after 12 seconds. Pick a point on the paper (any point less than 12 units away from the edge of Station A's circle) and label it "B". Now, draw a circle of radius 12 units around that point. The two circles should meet at two points. Since the earthquake traveled for 12 seconds to get to Station B, and 15 to get to Station A, it must be on one of those points because they are both 12 away from B and 15 away from A.
3) At this point, Station C would use its own detection time to find out how far away it was from the center. Station C will find out that one of the tow points we just mentioned is exactly that distance away: that point is the center of the quake!