This festival becomes available after you own a cow and it is Fall 4 of your first year or later. Neil sells the normal Cow at his animal booth for 10,000 G each. There are two colors of cows; one with large black spots and one with small black spots. Starting in Fall of year 2, or after you have had 3 baby cow births on your farm, Neil will start selling Jersey cows for 11,500 G each. Jerseys are either all-brown or brown spotted.
On the day of the festival, talk to Dunhill at the festival grounds to select the cow you want to use and the class you want to enter. You can't enter a sick, pregnant, or non-adult cow. You will have a better chance of winning if:
You enter a cow with a lot of Friendship Points (hearts)
The cow has zero stress
You brushed your cow that morning so it is clean
You enter a Jersey Cow instead of a normal Cow (the spot color does not matter)
The cow can produce more than 1 milk when milked
(Advanced class only) The cow can produce "Great" quality products
For the Beginner and Intermediate class, you can win simply based on the number of Friendship Points the cow has. You'll win the Beginner class at 361 Friendship Points (3.5 hearts = 350 FP) and the Intermediate class at 9 hearts. But for the Advance class, you'll need 10 hearts and some of the factors listed above. The other judgement factors affect the lower classes as well; for example, if you enter a normal Cow into the Beginner class that only has 3 hearts but 0 stress and is clean, then you still have a chance of winning the festival.
For simply participating in the festival you will earn 1000 FP with the villagers. If your cow is judged to be the winner, you will earn another 1000 FP with the villagers and you could receive a standard festival prize.
Neil will give you the choice of taking the item / blueprint / cooking recipe prize or you can take a special cow. This is the old-fashion bubble-body cow style from previous Harvest Moon games. The nostalgic style cow is a normal Cow and produces regular milk. You can only get one of these cows per Cow Festival victory but the bovine prize will be available regardless if you win the Beginner, Intermediate, or Advanced classes.