The easiest way to remember the difference, is that ales use top fermenting yeast strains, and lagers (it's a misnomer and will explain why) use bottom fermenting yeast strains. Under each of the two styles, you have many styles to be found within. Here is an example of some common styles of ales that you'll see....
Ales: Amber Ale, Pale Ale, India Pale Ale, Stouts, Porters, Strong Ales, Old Ales, Barleywine Style Ale, Dubbel, Tripel, Witbier, Biere de Garde......
Sometimes more styles within come into play by country, such as an American Pale Ale (Sierra Nevada Pale Ale) vs. English Pale Ale (Bass). Two common albeit VERY different beers and distinct styles of their own. Same goes for an American Imperial Stout (Speedway Stout) Vs. a Russian Imperial Stout (Old Rasputin). Interestingly enough, Russian Imperial Stouts are actually English in origin, but you'll learn the history of these beers along the way. The point is, that there are many styles within an ale, and they are quite broad but very identifiable once you've become accustomed to a particular style. The best thing to do next time you're at Bevmo (or wherever you shop) is to start out with 10 bottles of something different so you can begin to learn styles and pick out for yourself what makes them different from one another. Based on what you pick up, I would recommend drinking them in a certain order, and if you get to this PM me and I would be glad to help you out.
Usually your ales are going to be heavier in terms of Alcohol By Volume, body, and bitterness of the beer, but not always! A good rule of thumb too is to never let the color of a beer fool you. Just because it is lighter in color means absolutely nothing. If a beer is dark, that is by no means an indication that it will be heavy, boozy, bitter, or unlikable.
The word lager, is German for "to age". This refers to the brewing process of "lagers", since they used quite a bit of time to brew and ferment until they were ready for consumption. I forget the exact history behind it, but it had something to do with the Germans not having refrigeration back in the day, so they had to keep the barrels of beer underground in cool areas during the warm months to ferment so they wouldn't spoil from the heat. I think that is where the "to age" comes from, but don't quote me.
In actuality, the word lager
really isn't a style of beer. It confuses the hell out of many Germans that come to an English speaking country and are told that they have "to age" on their tap selection

In general, the Germans like to think of the typical "yellow" beer as either a Pilsner or Helles Lager. Helles is bright in German. They used the word helles to classify yellow beers, compared to some of their weiss (white) beers that they drink. But for all intents and purposes right now, the beer community has universally accepted "lager" as the style of beer that uses bottom fermenting yeast strains.
Here is an example of some common styles of lagers that you'll see....
Amber Lager, Pale Lager, Dark Lager, Pilsner, Bock, Doppelbock, Eisbock...
Again, some styles are assigned to certain countries. American Pale Lager (Moosehead) vs. Euro Pale Lager (Heineken). German Pilsener (Beck's) vs. Czech Pilsener (Pilsner Urquell).
You'll be surprised that a Doppelbock or an Eisbock (both lagers) will knock your socks off and perhaps more than many ales on the market. And remember, those doppelbocks and eisbocks are in the same family as your yellow (helles) beers. The best thing to remember is to never let color or appearance mislead you into thinking that it will be watered down or stronger/more bitter than you can handle.
I hope this helps !
And please remember, that neither Widmer or Pyramid are Hefeweizens! They're actually American Pale Wheat Ales. And if you hear somebody refer to either as a "hef", please slap them upside the head

Even worse, is when the server says "We have Bud, Miller, Coors, and Hef". AHGHGHGHGH !!!!
You wouldn't ask for a Stout if you wanted a Budweiser, right?