The mathematical equipment you'll need is a ruler and a compass.
When constructing a locus, you'll often need to draw circles, so the compass will be needed.
A locus is a line that is always the same distance from another line, or point.
A circle is a locus from a point (centre)
In constructing accurate locus, a compass is your best friend!
Draw a line equidistant from two points.
Suppose we have Point A and Point B.
We draw a semi-circle with a compass, one with your point at A and your pencil at B.
We do the same twith your point at B and your pencil at A.
They will meet at 2 points.
Draw a line, using a ruler, connecting them to get your equidistant line.
Bisect an angle.
To construct this, we want to find the 'bisector of the angle' which means we have to split the angle in to two equal halves, which would give a line that is equidistant to both the black line and the red line.
We use a compass to do this.
Draw an arc from the angle at O that crosses both lines.
Where it crosses these lines we shall label it C and D.
Place your compass, without changing its size, so that the point is on C and draw an arc
Do the same with the point on D.
Where these two arc's meet, draw a line with a ruler connecting it to O.
You know have bisected the angle and drawn an equidstant line.
You will be expected to be able to construct a range of standard loci, as well build loci for unfamiliar shapes, based on the rules you know.