Look up the heat transfer coefficient for the heat exchanger's coil material and the hot substance. A typical copper heat exchanger with water as the hot substance has a coefficient of 15 W/m^2 K.
Determine at what temperature the liquid will be flowing into the heat exchanger and your desired temperature for the liquid leaving the heat exchanger. The exit temperature can be as low as the ambient air temperature. Subtract the input temperature by the output temperature to get the temperature difference.
Calculate the necessary heat transfer rate by dividing the total amount of heat (in BTUs) you want to dissipate by the time frame of the dissipation (in hours).
Divide the heat transfer rate by the heat transfer coefficient times the temperature difference to get the coil surface area.
Determine the length of the coils by dividing the coil surface area by the coil circumference. For tubular coils, you can either measure the circumference by hand, or multiply the diameter by pi (3.141). For flattened coils, the circumference can be measured by hand, or estimated by multiplying the thickness by the width.