Can anyone explain to me me how long division works briefly or in detail? for 20pts?

If you have 1275 ÷ 4, you write it as shown, with 1275 on the inside and 4 on the outside. then you go digit by digit and find how many times 4 goes into the number. it goes into 1 zero times, so an imaginary 0 is put in the first spot above the 1. next, 4 goes into 12 three times, so 3 is written above the 2. After that, subtract 4×3 from 12, which leaves 0, and bring down the 7. 4 goes into 7 once with a remainder of 3, so a 1 is put up top and the 5 brought down next to the three. 4 goes into 35 eight times with a remainder of 3,so 8 is written up top. the 3 is the remainder, written as R3. so your answer is 1274÷4= 318 R3.
Hope this helps.