The "word" is not a viable unit of linguistic analysis. A word is most clearly defined by spacing/punctuation standards in the written language, but this conception of a word only loosely correlates with a phonologically motivated definition. And it doesn't work at all for languages with no writing system or whose writing system doesn't give words special status.
While a phonological definition of a word is possible for English, it's not so clear in languages with simpler phonotactics, such as Japanese. As far as I know, the only way to separate elements of a Japanese sentence phonologically is to look for the same vowel three times in a row. It's pretty safe to say that there is some level in the language that only allows two of the same vowel to occur in a row, but whether it's the word level or something else is unclear.
Even if the word is clearly defined for a given grammar, it's obvious that the same sort of processes that apply within a word (morphology) also apply when combining words within a sentence (syntax). The point is that, in any language, sentences can be analyzed as "big words" (as they almost must be for certain languages). In fact, it's not always clear where one sentence ends and the next begins. These divisions are conventional and somewhat arbitrary. One singular process is going on here. So is it a process of combination (meaning words, sentences, and everything else are all built out of morphemes, which are an indivisible primitive unit)? Not exactly.
Think of how you learn words. (And if you have children, think of how they learned words early on.) Just because you know how to use a given word (or phrase) doesn't mean you understand all its parts. Consider a word like "represent". Even if you know that "re-" means something like "again" or "in another way", you don't need this information to use and understand the word properly. In fact, a really strict interpretation of this word based on the parts you can see might actually be misleading! If you represent the first sound of "apple" with the letter A, you're not actually making two presentations; you're just conveying the same idea of /a/ with a visible symbol instead of an audible sound.
If you know just a little Japanese, you might know that "konnichi wa" means something like "hello", but you may not have known that "konnichi" can be broken down into two words: "kon(o)" (this) and "nichi" (day or sun). And you're probably not at all familiar with the meaning and usage of "wa". Actually, the "n(o)" in "kon(o)" might be analyzed as a separate word itself (a postposition or particle like "wa"). So how many words is "konnichi wa" in Japanese? One, just like "hello"? Two, as I've written it? Three? Four? As far as the Japanese language is concerned, it doesn't matter one bit. It only becomes an issue when you try to write Japanese using our Western writing system.
In general, you learn new words (like "phoneme") and only later (if at all) break them down into parts because of other similar words you've learned (like "morpheme", "phonology", "morphology", and "allophone"). From there, you can go out on a limb and say a word you've never heard before (like "allomorph") based on the overall pattern you've seen.
This is how language works. You hear something (probably a sentence) and connect it with some kind of meaning. Repeat this process quite a bit and you'll be able to generalize patterns. Apply the patterns, and you'll be able to say something new. You won't always sound proper (there might be a more standard way to communicate your idea), but the person you're talking to will probably be able to understand you. Over time, you'll hear (and understand) a ridiculous amount of language, allowing you to refine your generalizations and sound more standard.
For one reason or another, young children are better at spotting patterns in language and more reckless about applying them. This makes them sound childish, but more importantly, it allows them to race through the acquisition process, communicating pretty well along the way even with very limited knowledge of the language. So if you're trying to learn a language, try to act like a kid. Above all, be curious and reckless!