The best way to learn German is of course to live in a German-speaking country for a period of time. To interact with the locals in their language, to live the life in that environment. Even then, a basic knowledge of the structures and rules (the "grammar") of the language is necessary if you want to be able to speak well and be understood.
If you are a college student, the obvious answer is to take a class in German. The benefits of a class over self-learning are clear: you can interact with others in person. And since language is as much about speaking and listening as it is about reading and writing, having others to interact with is important.
If you are simply planning a trip and want to learn useful words and phrases, you might wish to check out the offerings of your local community college or university's continuing education program. Many offer short courses in German for travellers. If useful words and phrases are all that you're after, then a knowledge of the grammar is not as important, although it can't hurt.
More thoughts to come on the best way to learn German ...
Taking a language class is time-consuming, if in fact your goal is to learn to speak and understand, to read and write, a foreign language. But one thing that makes German easier for English speakers to learn than many other languages, and thus not be quite as time consuming as one might think, is the alphabet.
German usings pretty much the same alphabet as English. The only differences are German has variations on the vowels a, o, and u namely ä, ö, and ü. Sometimes you see cutesy English product names that add the two dots for effect. But in real German, the two dots (called an "umlaut") are not at all decorative; they make the vowel sound different. German a is pronounced roughly like the a in English "father", while ä is pronounced sort of like the a in English "day". (Not exactly, but the details of that are for another discussion.)
German has one letter that doesn't even resemble English: it's the ß (called an "es-tset"). It looks sort of like a Greek beta (a beta looks like this β) or even a funky letter B, but has nothing to do with either. It is pronounced just like the s sound in the English word "hiss". By and large, the German pronunciation of most letters is similar to English, though not always. This, too, makes learning German easier than, let's say, learning a language with a different writing system, such as Japanese. Another way German is easier is in the great number of cognates. Cognates are words that two or more languages share in common. The word "hand" is Hand in German, spelled the same, pronounced similarly, and mean the same thing. Cognates are not always spelled the same. For example, the word "glass" is Glas in German, which is pretty easy to recognize. Or take the word "grass" Gras, or "house" Haus, or "mouse" Maus. There are thousands of similar correspondences between the two languages. But be aware, they are not always the same meaning. For example, the German word Gift means "poison", and the German word Mist means "manure". In all, though, there are many similarities between English and German. Once you become accustomed to the patterns of correspondences, you can almost guess what many words or phrases mean.
