Alright, we set it up with 7 in front of a long radical sign with 3566 inside.
Does 7 go into 3? No.
Does 7 go into 35? Yes, so 5 goes up top(above the 5 of 35). 5 x 7 = 35, so we subtract 35 - 35 and get 0.
We bring down the 6. Does 7 go into 6? Noooo, so a 0 goes above the first 6. 0 x 7 = 0, so 0 goes under 06 and 6 - 0 = 6.
Bring down the 2nd 6. Does 7 go into 66? Yep, so 9 goes above the 2nd 6. 9 x 7 = 63, and 66 - 63 = 3.
We have no more digits, so our quotient is 509 and our remainder is 3.