Collect the information you need to do the calculations and plot out the shape of the ellipse, the locations of the hour points on it, and the 12 gnomon locations you will establish (assuming you will use it for a year). The required information includes the latitude and longitude of the sundial location as found on a map or by using a GPS device, and a table of solar declinations.
Perform the necessary calculations using a calculator with trigonometrical functions. Assume that the length of the major axis (M) on your plot will be 10 inches. Calculate the length of the minor axis (m) by multiplying the sine of your latitude (l) by 10. Make a table of x-y coordinates for your ellipse for every 15 degrees of angle (t) from zero to 90 degrees. Use M/2 x cosine (t) for the x values and m/2 x sine (t) for the y values. Calculate the minimum height (h) for your gnomon by dividing m/2 by tangent [(l)-23.4]. Note that this is the June 21 shadow, the shortest of the year.
Plot the major and minor axes of your ellipse on a sheet of graph paper. Designate the point where they cross the origin (O). Then plot the x,y values at the 15-degree points for one quadrant of the ellipse. Use a protractor and ruler to measure the angle from the minor axis and the line length for each point. Make a table of hour points. The end of the minor axis is noon and the endpoints of the major axis are 6 a.m. and 6 p.m.
Calculate the gnomon locations for your sundial and make a list of them for the first of each month using the values from the table of solar declinations. The gnomon distance from point O (z) along the minor axis for each month is M/2 x tangent (d) x cosine (l). Note that these distances will be positive and negative with June to the north.
Find a suitable, sunny site for your sundial. Place the gnomon exactly upright at the center of what will be the ellipse. Mark the location of the shadow of the gnomon at exactly 12 noon. This is the alignment of the north-south (minor) axis (compensated for your position in your time zone). Mark the east-west (major) axis exactly perpendicular to the north-south axis. Measure the length of the east-west axis that you will use as your sundial.
Multiply all your calculated distances by the ratio of the actual length of the east-west axis to the major axis on your plot. Mark the length of the north-south axis using a measuring tape. Take a board and mark the half-lengths of the axes on it from one end: and then, keeping the "long" mark on the north-south axis and the "short" mark on the east-west axis, rotate the board and use the end of it to draw your ellipse. Lay out the positions of the hour points and identify them. Mark the gnomon locations along the north-south axis and identify them. Place the gnomon at the correct position according to the date and you will have a simple but functional analemmatic sundial. Further refinements depend on the purpose for its construction.