The most effective and food-safe method is iced water
A very safe method is to put the frozen meat in the fridge. It will defrost (eventually), but never exceed ~3C (the temperature of an average fridge), so it remains safe. The problem is that it can take a day or more to achieve this.
It takes that long to defrost in the fridge because air is very poor at transferring heat. To explain, imagine your oven has been heated to 100C, and that you have a pot of boiling (100C) water on the stove. The air in the oven and the water on the stove are both at the same temperature (100C) — but because air is such a poor heat conductor, you can safely put your hand in the oven but it would be catastrophic to put it in the water.
So, it can take ages for the air in the fridge to transfer heat to the meat and defrost it.
The worst thing to do is to try and speed this up by putting the meat on a counter-top at room temperature. And it still takes ages anyway.
The best and safest method is to put the frozen meat in an ice-water bath. This works for the same reason that you didn’t chose to put your hand in the boiling water (I hope) — water is a great conductor of heat and will thaw the meat quickly.
Method: Run some cold water into a bowl or small sink, and add plenty of ice (a 50:50 ratio is ideal). If the meat was vacuum packed before being frozen (recommended), then just pop the bag in the bath. If not, take the meat out of whatever it was wrapped in, and put inside a waterproof plastic bag (something like a ziplock) and leave the top open. Slide the bag into the water keeping the opening above water level, and use water pressure to expel most of the air from the bag around the meat. You want as little air left as possible so that most of the meat is in contact with the water (via the plastic) and the meat does not float. Let sit until thawed — I predict you will be surprised how fast and effective this is.
The water in the ice-bath cannot be below 0C (or it would be ice), but is kept cool by the ice (it usually sits around 3C — fridge temperature). So it is equivalent to thawing in the fridge, but using water instead of air and so very much faster.
You might think that warmer water would be better, but surprisingly it isn’t that much faster, and of course the outside of the meat is no longer at a safe food temperature.