I have tried both the classical and the New Cyanotype processes and find the new process, developed by Mike Ware, to be much easier to work with. You can read Mike Ware's detailed description at The New Cyanotype Process. I have copied the formula and step by step preparation from that site and provide it here.

Sensitizer Chemicals needed
Ammonium Iron (III) Oxalate 30.0 g
Potassium Ferricyanide 10.0 g
Ammonium Dichromate (25% solution) 0.5 cc
Distilled water to make 100.0 cc

Preparation of Sensitizer
The preparation of this sensitizer solution calls for a bit more experience in chemical manipulation than is required to make a traditional cyanotype sensitizer, so don't undertake it unless you are fairly confident. This work should be carried out under tungsten light, not fluorescent or daylight. Please note that all the chemicals are poisonous!

1. Using a pestle and mortar, finely powder 10 g Potassium Ferricyanide. Wear a dust mask, to avoid inhalation of the powder, and pay attention to thoroughly completing this step, which is indicated when all the red crystals are crushed to a yellow powder.
2. Heat ca. 30 cc distilled water to ca. 50º C and dissolve in it 30 g Ammonium Iron (III) Oxalate.
3. Add 0.5 cc 25% Ammonium Dichromate solution, (previously prepared by dissolving 5 g of the solid in distilled water and making up to a final volume of 20 cc). Mix thoroughly.
4. To the solution, while it is still hot, add the 10 g of finely powdered Potassium Ferricyanide in small portions with vigorous stirring; few (or preferably no) red crystals should be seen, and green crystals will begin to appear. Set the solution aside in a dark place to cool and crystallize for about one hour.
5. Separate most of the liquid from the green crystals by filtration. The green solid (Potassium Iron (III) Oxalate) is disposed of safely (poisonous!). The volume of solution extracted should be ca. 30 to 33 cc.
6. Make up the olive-yellow coloured solution with distilled water to a final volume of 100 cc. The sensitizer can be made more dilute (e.g. up to 200 cc): it will be faster to print, but yield a less intense blue.
7. Filter the sensitizer solution and store it in a brown bottle kept in the dark; its shelf life should be at least a year.

Personal Notes:

Sensitizer:
I used sensitizer that was mixed three years ago and it worked fine. With the sensitizer that I mixed three years ago and some that was freshly mixed I had problems with fogged highlights and staining in the masked area around the image. I found that by adding citric acid and potassium dichromate to the sensitizer before coating I got very clear highlights and the staining in the white border area was eliminated.

Additives:
Potassium Dichromate (1%) 1 drop per 10 drops of sensitizer
Citric Acid (12%) 1 drop per 10 drops of sensitizer

Coating:
I give a single coat with a glass rod. By adding one drop of Tween 20 (5%) per 10 drops of sensitizer I get better results. I have coated and dried as many as four sheets of paper at the same time and used them within an hour and had no problems with staining.

Papers:
I experimented with the following papers with mixed results.

Stonehenge: Good contrast and D-max but grainy.
Rising Gallery 100: Good contrast and D-max but grainy.
albireo Good contrast and D-max and not grainy at all. Gave the best results.
Whatman Hanga: Good contrast and D-max and not grainy.

Wet Processing:
After exposure I place the prints in a 2% citric acid solution and agitate them for one minute. By now they are almost completely cleared. I next move the prints to a tray of water and agitate. My tap water is alkaline having a pH of about 8 so I acidify it with one gram of citric acid per five liters of tap water to bring the pH to about 5.5. I change the water every minute for four minutes. I next run the prints through a weak hydrogen peroxide solution (about .3%) for 15~30 seconds to bring the reversed shadow tones to a deep blue. Finally the prints are rinsed in tap water. I monitor this final step closely because the alkalinity of my tap water gradually bleaches cyanotypes.

Sodium Bicarbonate Reducer (Bleach):
Sodium bicarbonate bleaches, and at the same time, causes the color to shift to a very deep blue. Initially it seems to act more on the highlights than on the shadows. A saturated solution can be used to clean up splatters and sensitizer edge lines in the white borders. For general bleaching I add two teaspoonfuls (about eight grams) to one liter of water.