Label the digit immediately before the decimal point as the units digit. Moving left, label the next digit as the 10s digit, the 100s digit, the 1,000s digit, etc. Another way to think of this is that a digit that is x digits to the left of the decimal point is the 10^(x-1)s digit.
Label the digit immediately to the right of the decimal point as the 10ths (1/10) digit. Moving right, label the next digit as the 1/100 digit, the 1/1,000 digit, etc. Another way to think of this is that a digit that is x digits to the right of the decimal point is the 1/(10^x) digit.
If a number is given in scientific notation, write it out in regular notation and use the rules above. For example, 6.25 x 10^-4 is equal to 0.000625 in regular notation.
To add or subtract decimals, line up the decimal points in each number so that each place value is lined up with the same place value of the other numbers. Add the digits as you would with whole numbers. Write the decimal point in the answer so that it lines up with the decimal points of the other numbers.
To multiply decimals, proceed as you would with whole numbers. Count the digits behind the decimal point in the numbers that were multiplied. Write the decimal point in the answer so that that number of digits is behind the decimal point. The decimal point in the answer determines the place value of each digit in the answer.
To divide decimals, move the decimal point over just enough spaces to that all digits are before the decimal point in the divisor. Divide as you would with whole numbers. Write the decimal point in the answer so that it lines up with the decimal point in the dividend. The decimal point in the answer determines the place value of each digit in the answer.