If you've been doing your joint mobility drills before working out and/or stretching, you should be able to determine which side is tighter pretty easily and work accordingly. And if you know beforehand that something is tight, you can work the opposite side for these mobility drills.
Why stretch the good side first, especially when some will tell you to do the opposite? Well, in the interest of correcting imbalances, we need to know how far we should be moving before we can figure out how far we do need to move.
As Mike Robertson points out:
Stretch the good side first to determine the range you want to achieve on the other side. Then simply stretch the tighter side until you can achieve that same range. It may take only a little while longer (or significantly longer) to achieve, but making your stretching program outcome based ensures that you’re doing everything possible to iron out imbalances.Ironing out imbalances is a good thing to keep in mind - imbalances are usually where problems start and get worse....
While injuries or time constraints might not allow you to achieve a balanced stretch on both sides during every stretching session, working the good side first will also "open up" the muscles, making it easier for you to increase range of motion especially for joints where the muscles either meet or cross over (hips and shoulders mainly).
You'll also be more aware of whatever limitations you might have coming into any given training session.