Let the repeating decimal be (x)
Identify the non-repeating part and the repeating block
Multiply (x) by a power of 10 that moves one full repeating block to the left of the decimal point
Multiply (x) by a power of 10 that moves only the non-repeating part to the left of the decimal point, if needed
Subtract the two equations
Solve for (x)
Simplify the resulting fraction to lowest terms