I'll start with the basics. Yeast eat sugar, piss alcohol, and fart carbon dioxide. Not all sugars are the same. In order of complexity, Fructose, Sucrose, Glucose, Maltose, and Maltotriose are the 5 common types of sugar found in wort. The less complex they are, the easier they are for yeast to metabolize. For a high alcohol beer, you generally want to maximize the yeast's potential to feast on all of those different types of sugar.
Attenuation is basically the percentage of sugars that the yeast can ferment. If you take two identical worts and use a highly attenuating yeast (such as American Ale yeast, or High gravity yeast, etc) in one and a low-attenuating yeast (such as some English strains) in another, the first beer will wind up with more alcohol. It will also be perceived as "drier" tasting and less sweet, since more of the sugars have been consumed. But the variation of yeast from low to high attenuation isn't all that great. Changing yeast strains alone won't turn a normal beer into a high gravity strong beer, it'll just add a little extra maltiness or sweetness. To really alter the gravity, you need to add more fermentables... more sugar. And if you're doing that, you might as well use a highly-attenuating yeast. Mathematically, the difference between a high and low attenuating brewers yeast is not much. However it makes a much substantial difference in terms of flavor. Using a low-attenuating yeast in a strong beer is going to leave an excessive amount of sweetness behind. So high gravity (strong) beers will generally use a yeast with high attenuation.
So using a more attenuating yeast will increase your ABV a little bit. So, too, will adding more fermentables. More DME, LME, Sugar, etc will give the yeast more to munch on, and therefore generally give you more alcohol. But the higher you go, the more problems you run into. Yeast can't live in a highly alcoholic environment. Alcohol is a waste product to them. Of course, some yeasts do better than others. A yeast with a low alcohol tolerance may start to struggle as it gets above about 4%ABV. A highly tolerant yeast will probably start to struggle around 9%. However, there's tricks and things you can do that will allow either yeast to perform a LOT better.
1. Pitching an adequate amount of yeast so they do not get stressed.
2. Providing oxygen at the beginning of fermentation to encourage cellular reproduction. Yeast use oxygen to reproduce. Giving them a bunch of oxygen will result in them multiplying, giving you more yeast to finish your fermentation.
3. Controlling temperatures. Yeast will fall out of suspension and go dormant if it gets too cold. They will produce off-flavors or possibly die if too hot. Generally, ale yeast reproduce best in slightly warm environments, but produce the best flavors in temperatures that tend to fall a bit on the cool side for what humans find comfortable. Lager yeast like it a bit cooler than that, but still generally in a relatively comfortable range, the 50-75 degree range is generally good depending on the yeast. Also, rapid changing of temperatures (such as a sudden drop in air temp, or particularly, putting a cold vial of yeast into a warm fermentor) will cause a lot of the yeast cells to die from shock, resulting in much less yeast than anticipated.
4. Controlling the introduction of sugars. Adding a lot of pure sugar to a beer at the beginning may result in a stuck fermentation, as the yeast will eat all the "easy" simple sugars and will lose the ability to eat the complex sugars which will just leave the beer overly sweet and under-attenuated.
5. Providing nutrients. Generally, your typical wort is rich in nutrients, but if you're making a mead, or a beer with a lot of sugar or other unusual ingredients, you may need to add a yeast nutrient in order to ensure yeast health.
With these factors, and a few others that I am probably forgetting, we can take that 4-9%ABV range for typical brewing yeasts and push it to more like 8-16%ABV. Somewhere between those figures is typical for most brewers yeast under normal conditions. And, of course, there are a few yeasts out there that can go a bit higher, typically with lots of help and intervention, possibly including pitching multiple batches of healthy active yeast into the same beer at different time intervals.
The highest gravity beer I ever made was around 18%. It took about 8 months of care and feeding. And I knew a lot less then than I know now. I'm sure I could hit the low-to-mid-twenty percent range if I really had a need to.