Terms used in the manual:

• Object—point, circle or line
  
• Construction—one of the simple constructions that are supported by Plane (e.g. drawing line connecting two points)
  
• Master point—point that has independent variable coordinates.

First construction must be a master point. To create such point one should press button and then left-click somewhere on the client area of the window, where the point should be positioned. A dialog will pop-up asking for symbolic values of the point's coordinates. The symbolic values cannot exceed in length 3 characters and should comply with Mathematica syntax, if one intends later to simplify expressions with the software. Three characters should suffice to create thousands of unique expressions.

and are used to navigate through objects or constructions. Selected objects are red.

button is used to select a highlighted construction or an object to add a construction or to obtain or change a parameter of the object.

With button pressed user can move master points with arrow keys. The rest of the diagram will change accordingly.

Following buttons are used to create constructions:
line connecting two points
circle
point dividing segment in given ratio. The dialog will accept only integer values in the interval (-32K;32K). Obviously, the sum of entered values cannot equal 1.
perpendicular drawn from a given point on a given line
point of crossing of two lines
points of crossing of a line and a circle
points of crossing of two circles

is used for symbolic manipulations with objects. With this button pressed user may navigate through all objects with and and obtain or change objects' symbolic parameters. For example, when a point is selected ( is pressed) and will appear. Pressing will (except in the case described further) copy the expression corresponding to the x-coordinate of the point to the clipboard. The expression in the clipboard would be ready to be used in the Mathematica frontend. If the selected object is a line, , and will appear. The expressions obtained by pressing these buttons will be the parameters of the line equation a×x+b×y+c==0. Additionally, if the line was drawn through two points, will yield the distance between the two points. In the case of circle, values in , and will correspond to the x and y coordinates of the centre of the circle and the radius of the circle. If one presses before first construction is added this button will be disabled and the application will not calculate expressions until the application is restarted. ("no expressions" mode)

When the button is pressed and the selected object belongs to the last construction switch-button will appear. When the button is not pressed, it shows (which is default), and when pressed, it shows . Pressing buttons , , , , , or will "get" expressions to the clipboard, when the switch shows , and "set" the parameter of the object to the expression in the clipboard, if the switch shows . After the parameter was set, the application will use this new expression in all further calculations. When setting a parameter from the clipboard, Plane does not check whether the expression in the clipboard complies with Mathematica syntax. That is why one should first ensure that the expression is "edible", before setting the parameter. Possibility of changing object parameters was added to the interface to enable user to simplify expressions generated by Plane and make substitution with simplified expression saving memory and CPU time. In some cases without such simplification one will be unable to reach the last construction, because the system will run out of memory and the application will crash.