Convert the desired number from its original base to base 10 by adding the value of the digits based on their positional notation. For example, 312 in base 5 consists of a 2 in the units column, a 1 in the 5's column and 3 in the 25's column. To find the base 10 equivalent, simply add the total values of each column: 2 + 5 + 75 = 82.
Divide the base 10 number by the value of the base you wish to convert it to. Keep a note of the remainders and continue dividing until you reach an answer of zero. For example, to convert 82 in base 10 to base 6, you would first divide by 6 to get 13 with a remainder of 4. Next, divide 13 by 6 to get 2 with a remainder of 1. Finally, divide 2 by 6 to get 0 with a remainder of 2.
Write out your remainders in reverse order to find the result of the conversion. For example, 82 converted to base 6 becomes 214.