The first step in long division involves a separate division problem, although a much simpler one than the problem as a whole. For example, divide 216 by 6. You'll write the 216 under the long division bar and then write the 6 out to the left. There aren't any 6's in 2, so you move a digit to the right in the dividend. Now, divide 21 by 6. There are 3 6's in 21 (6 * 3 = 18), but not 4 (6 * 4 = 24, which is more than 21). So, you write a 3 on top of the bar, just above the 1 in 216.
Now, multiply the 3 on top by the 6 out in the divisor. Write the result (18) below the "21" in 216. Then, write a minus sign out to the left of the 18.
You'll want to subtract 18 from 21. You'll get 3. Now, bring down the next number after the "21," which is 6, and write it next to the "3" making "36." Divide the 36 by 6. The result is 6. Write "6' up next to the 3 on top of the bar, and you'll see 36 up there. Multiply the "6" by the "6" in the divisor, and you'll get 36 again. Write that down below the 36 and subtract to get zero. 216 / 6 = 36.
If you're dividing 802 by 46, traditional long division can require some head-scratching during the multiplication process. Multiply 46 * 10 to get 460 and 46 * 2 to get 92. Now, you're going to start subtracting, which is simpler than multiplying.
Start out by subtracting multiples of 10.
802 - 460 = 342. You can't subtract 460 again, but you know that you have at least 10 multiples. Now subtract sets of 92:
342 - 92 = 250.
250 - 92 = 158.
158 - 92 = 66.
You were able to subtract six more multiples, and you have 66 left over as your remainder. So the answer to 802 / 46 = 16 Remainder 66.
Are you wondering what remainders are? As you just saw, not all long division problems resolve out to a zero at the end. If the traditional-method example had divided 218 / 6 instead of 216, you'd have a "2" at the bottom. Because 6 does not go into 2, 2 would be your remainder, or amount left over. The answer would be 36 R 2 (36 Remainder 2, or 36 2/6, or 36 1/3 when simplified).