In morpheme-based morphology, word-forms are analyzed as sequences of morphemes. A morpheme is defined as the minimal meaningful unit of a language. In a word like independently, we say that the morphemes are in-, depend, -ent, and ly; depend is the root (linguistics) and the other morphemes are, in this case, derivational affixes. In a word like dogs, we say that dog is the root, and that -s is an inflectional morpheme. This way of analyzing word-forms as if they were made of morphemes put after each other like beads on a string, is called Item-and-Arrangement.
The morpheme-based approach is the first one that beginners to morphology usually think of, and which laymen tend to find the most obvious. This is so to such an extent that very often beginners think that morphemes are an inevitable, fundamental notion of morphology, and many five-minute explanations of morphology are, in fact, five-minute explanations of morpheme-based morphology. This is, however, not so. The fundamental idea of morphology is that the words of a language are related to each other by different kinds of rules. Analyzing words as sequences of morphemes is a way of describing these relations, but is not the only way. In actual academic linguistics, morpheme-based morphology certainly has many adherents, but is by no means the dominant approach.
Applying a strictly morpheme-based model quickly leads to complications when one tries to analyze many forms of allomorphy. For example, the word dogs is easily broken into the root dog and the plural morpheme -s. The same analysis is straightforward for oxen, assuming the stem ox and a suppletive plural morpheme -en. How then would the same analysis "split up" the word geese into a root and a plural morpheme? In the same manner, how to split sheep?
Theorists wishing to maintain a strict morpheme-based approach often preserve the idea in cases like these by saying that geese is goose followed by a null morpheme (a morpheme that has no phonological content), and that the vowel change in the stem is a morphophonological rule. Also, morpheme-based analyses commonly posit null morphemes even in the absence of any allomorphy. For example, if the plural noun dogs is analyzed as a root dog followed by a plural morpheme -s, then one might analyze the singular dog as the root dog followed by a null morpheme for the singular.