We're dividing 9566 by 4 
We're looking to find how many times 4 goes into 9566.

On to step 1:
9 divided by 4 is 2 with a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we subtract 8 from 9, we get 1.
Take the next digit (5) from the dividend and append it to 1, then repeat: 15 / 4

Step 2:
4 goes into 15 3 times with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 23.0
Subtracting 12 from 15 leaves us with 3.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 4

On to step 3:
4 can be fit into 36 9 times, resulting in a remainder of 0.
The next digit of our result is 9. 
Result so far: 239.0
Deduct 36 from 36 and we're left with 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 4

Moving on to step 4:
4 can be fit into 6 1 times, resulting in a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 2391.0
Subtract 4 from 6 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 5:
The number 4 fits into 20 5 times, leaving a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 2391.5
If we take 20 away from 20, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 6:
When dividing 0 by 4, we get 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 2391.5
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 7:
When dividing 0 by 4, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 2391.5
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 2391.5, and the remainder is 0.0.