There are two primary ways to think about how to multiply decimals. Both of these ways are demonstrated step by step above.
The first method is called estimation. Begin by writing out your original problem. Once you have done this, remove the decimal from the original numbers and multiply them. Then, round any decimal numbers and multiply again. The final step is to place a decimal back into the answer from the second step in the position which makes the result closest to the estimate from the third step.
The second method is called place values. Rewrite each decimal number as a whole number divided by a power of ten. Then multiply the tops and bottoms to get a fraction. The denominator is a power of ten. Finally, move the decimal place over according to which power of ten is in the denominator.