This thesis is concerned with a central question in any construction-based, usage-based theory of language acquisition: how children get from more concrete and item-based constructions to more abstract constructions. The overall approach places central importance on meaning and the role of cognition to categorise chunks of linguistic experience into conventional grammatical units. Chapter 1 outlines the historical and conceptual foundations in the field of language acquisition and justifies the usage-based approach taken in this thesis. Chapter 2 then considers what usage-based theories mean when they characterise language acquisition as 'a developing inventory of constructions that are more-or-less schematic'. By bringing together findings from categorisation and analogy, social cognition and construction grammar the aim is to show how argument-structure constructions are learnable. Chapter 3 investigates the topic of how infants construct grammatical categories by taking a cross-linguistic look at the transitive construction in the context of a prototype theory of categorisation. Chapter 4 applies the theoretical investigations of previous chapter to an empirical experiment, specifically, making developmental comparisons of the prototypical semantics of the transitive construction in English. Chapter 5 considers further the role of different cues in children understanding of argument-structure constructions by examining the role of pronoun frames in early comprehension of transitive constructions in English. Chapter 6 focuses on how infants and mothers actually use language in a corpus study. It begins by looking at the role of skewed distribution and cognitive anchoring in schematising the Subject Verb Object construction in English. It then presents a usage-based acquisition model of argument productivity in subject-verb-object constructions. Chapter 7 concludes the thesis by summarising the experimental and theoretical work; identifying some cognitive features and properties of the input that seem to be important in all the studies; providing a critique of the usage-based approach; and finally, suggesting some key issues that future work in usage-based approaches to the acquisition of grammar needs to address.