The need for interpretable and accountable intelligent systems grows along with the prevalence of artificial intelligence applications used in everyday life. Explainable intelligent systems are designed to self-explain the reasoning behind system decisions and predictions, and researchers from different disciplines work together to define, design, and evaluate interpretable systems. However, scholars from different disciplines focus on different objectives and fairly independent topics of interpretable machine learning research, which poses challenges for identifying appropriate design and evaluation methodology and consolidating knowledge across efforts. To this end, this paper presents a survey and framework intended to share knowledge and experiences of XAI design and evaluation methods across multiple disciplines. Aiming to support diverse design goals and evaluation methods in XAI research, after a thorough review of XAI related papers in the fields of machine learning, visualization, and human-computer interaction, we present a categorization of interpretable machine learning design goals and evaluation methods to show a mapping between design goals for different XAI user groups and their evaluation methods. From our findings, we develop a framework with step-by-step design guidelines paired with evaluation methods to close the iterative design and evaluation cycles in multidisciplinary XAI teams. Further, we provide summarized ready-to-use tables of evaluation methods and recommendations for different goals in XAI research.