Algorithms are used to make automated decisions that can affect individuals in numerous domains. The General Data Protection Regulation (GDPR) of the European Union (EU) has granted citizens some rights regarding solely automated decision-making (SADM), including obtaining an explanation of such processing. It is unclear, however, how organizations should support people in effectively exercising such rights. We conducted an online survey to understand people's perspectives on SADM. We found that our respondents had several misunderstandings about the SADM right, such as opt-out of SADM ahead of time. We also identified various attributes of SADM that our respondents desired to understand, including new attributes (e.g., actionable information about what they can practically do to improve future decision outcomes) not covered by implementation guidelines of the GDPR. Our respondents also anticipated many challenges with SADM, including not knowing when SADM is applied to them. We discuss design implications of our results on how to support people in coping with SADM, for instance, the design of icons to represent SADM processing and explanation templates that cover a common set of attributes and can be personalized to explain a specific SADM decision.