How would I describe a step-by-step procedure for adding two fractions with different denominators?
The first thing you need to do is make the denominators the same. You do this by finding their lowest common multiple. We'll use this as an example:
The first multiple of eight that three can evenly divide into is 24. So, we change each denominator to 24, also multiplying each numerator by the number we had to multiply the denominator by to reach 24 (I hope that made sense, I can't think of a better way to articulate it). We end up with:
Add the numerators; the denominator remains the same: