The criss-cross pattern of tightening lug nuts is an unstated law that is widely advocated for a good reason. It is an inexplicit yet widespread practice that is followed by everyone from your local mechanic to the guy stuck in the middle of the highway attempting to replace his flat. However, even today, many people are not aware of the scientific reason behind this peculiar practice and that is exactly why we're here.
Here's the secret: The simple reason behind the star pattern of torquing your lug nuts is to reduce wheel flexing and shifting. You see when you tighten a single nut, it keeps getting tighter and tighter till the point the wheel mounting face (what you're tightening against) gets stuck to the hub.
The thing is, if you get one corner (one lug) nice and tight and you naturally go to the next one in a clockwise or anticlockwise direction, there is a huge chance that the wheel will not stay straight and will flex in a way that leaves the initial lugs you tightened a little loose. This is why its always recommended that you tighten lug nuts across one another to minimise chances of wheel flexion.
Think about it. Are two lugs on one side of the wheel better to hold the wheel straight and evenly in place or are two lugs at opposite ends of the wheel better?
Tightening the lug nuts in a criss-cross fashion makes sure that every side of wheel face is evenly stuck to the wheel hub throughout the process of tightening. This reduces the likelihood of things shifting and flexing, which means that the nuts will stay tight even after you torque them. It shouldn't be that one part of the tyre is extremely snug with the wheel hub while the other is completely loose. This increases the chances of wheel flexion and movement and there are very high chances that your initial lug nuts will become loose as the wheel shifts.
An average car weighs about 4000 pounds, all of which has to be carried forward by your tyres. If you think about it, your tyres are bolted to the vehicle only by these lug nuts and that's pretty much it. These limited number of tiny lug nuts have to tolerate shearing forces from the 4000 pound car when it moves forward or brakes.
Unevenly torqued wheel lug nuts are extremely detrimental to your vehicle. Uneven brake pad deposits, irregular brake and rotor wear, vibrations during braking are just some of the issues that can crop up due to sub-optimal lug nut fitting. Such vibrations from the brake are also sometimes misdiagnosed as a tyre issue.
You can use the diagram in the beginning as a reference for tightening your lug nuts in the right pattern. Follow the arrow and numbers to the T along with the right torque level to get the perfect fit for your lug nuts. Don't forget to do another round of checks after you've tightened them just to be safe.
Tighten In the Air or on the Ground?
Ideally, you should do two rounds of tightening the lug nuts. The first is done when the wheel is in the air simply to fix the lug nuts enough so that the wheel is stable and straight. The second is when the car wheels are on the ground and requires stronger tightening until the optimum torque rating is reached.
Never perform the final tightening of your lug nuts while your car is in the air. The simple reason behind this is that your tyre gets a much better and stable platform when it's on the ground which again reduces chances of wheel flexion. Only when you have new brake pads, should you tighten the nuts snugly before you lower the vehicle back to the ground. But even then, just to be safe, you should perform another round of tightening once the car is on the ground.
Note: It can be quite tempting to stand on the nuts to tighten them, however, this is not a good idea at all. Tight lug nuts are great, but over-tightening lug nuts can cause you a lot of trouble in the future. There is also the risk that you might break the nut and wheel stud or slip off the wrench and injure yourself. So please refrain from such practices.
Speaking of over-tightening, you need not worry about this when you use your hands to screw the lug nuts. Most instances of over-tightening happen due to overusing an impact driver or a pneumatic impact driver. The benefit of using your arms makes it nearly impossible to over tighten them to that degree!