When it comes to the sweetness level of a wine, most people think of wines as being either sweet or dry (dry is used to mean many things, but properly it only refers to the sweetness level of a wine, ie a dry wine is one that is not sweet). Actually the sweetness level of a wine takes on many forms. Sommeliers usually categorize wines by their sweetness level the following way:
Sweet - sweet and rich, like a dessert wine
Semi-Sweet - Where most wines described as 'sweet' fall into. Spatlese Rieslings are one example, or our ever popular Voulet Casorzo. Many of the sweet (but not dessert) wines made in Virginia are semi-sweet.
Off-Dry - Probably where the majority of wines consumed by the American public fall into. Many wines people describe as dry are actually off-dry. They have a touch of sweetness to them because that is what our palate is used to. You may have noticed that French reds tend to taste harsh, for lack of a better word, compared to California reds. It's the sugar.
Dry - Very little residual sugar (the sugar left in the juice after most has been fermented into alcohol). This would describe many whites, such as Sauvignon Blanc, or reds such as Cabernet, Malbec, or Pinot Noir. It depends on who's making the wine, of course, but dry wines will truly taste dry.
Bone Dry - little to no residual sugar. Not very common in the U.S., since bone dry wines are not pleasing to a lot of people (we like them). Champagnes labeled as "Extra Brut" are bone dry. So are some other styles of wine, especially from Europe, such as Rieslings from Alsace (did you think all Rieslings were sweet? Sorry for all the parenthetical statements).
These are not technical terms but terms used by retailers and restaurant operators to describe wines. If you want a good recommendation, you are better off using one of these than simply asking for a sweet or dry wine.