The explosive growth of artificial intelligence and high-performance computing workloads has exposed fundamental scalability limitations in traditional monolithic system-on-chip designs, driving industry adoption of chiplet-based architectures that decompose complex systems into modular dies for heterogeneous integration. High Bandwidth Memory generation 4 promises substantial improvements in aggregate bandwidth and energy efficiency, yet integrating HBM4 stacks with chiplet processors introduces multifaceted challenges spanning die-to-die interconnect design, physical layer robustness, package-level signal and power integrity, thermal management, and runtime system control. This article presents a comprehensive methodology for chiplet-HBM4 integration that harmonizes protocol-level optimizations with adaptive physical layer techniques, thermal-aware package design, hierarchical power delivery networks, and telemetry-driven runtime adaptation. A unified verification framework bridges digital performance models with analog signal integrity and thermal simulations to ensure pre-silicon predictions align with post-silicon measurements, enabling first-pass silicon success. Experimental evaluation across representative AI training, inference, and HPC workloads demonstrates that cross-layer co-optimization combined with intelligent runtime control delivers substantial gains in latency reduction, energy efficiency, and operational availability under realistic environmental variations. The article establishes practical design principles and reusable methodologies for multi-terabyte-per-second memory systems targeting deployment in next-generation AI accelerators and scientific computing platforms.