The recent advancement in Artificial Intelligence (AI) has paved the way for the wide adoption of new tools and techniques in numerous disciplines. Galleries, Libraries, Archives, and Museums (GLAMs) are adopting AI-based solutions to efficiently organise, analyse, and utilise their digital collections. The application of AI-based solutions in GLAMs is mainly based on the foundational work librarians, archivists and museologists did in digitising their collections in a machine-readable format. Following the digitisation effort, the organisation of the digitised resources by integrating metadata that provides useful information to properly utilise the resources paved the way for the application of AI solutions. Nowadays, GLAMs have started exploiting the technology in digital image processing, semantic enrichment, and interlinking of historical and cultural collections including images, photographs, drawings, sketches and other archival collections. To efficiently utilise these AI solutions and assist non-technical experts who are working in GLAMs, a methodology that works not only for AI experts but also for all stakeholders is a necessary condition. In this paper, I discuss a methodology that has been used in projects that are dedicated to the organisation of cultural heritage collections using AI-based solutions. The methodology has three phases: the preparation phase focuses on domain understanding, acquisition of target collection, and ontology selection; the analysis phase focuses on semantic enrichment (annotation) and knowledge graph generation; the deployment and exploration phase focuses on focuses on the implementation of the solutions and exploitation of the semantically enriched AI-Ready resources using the AI-based solutions. This paper will further present two case studies where the methodology is applied and presents the lessons learned from the two projects.