Document-level relation extraction (DocRE) is the task of identifying all relations between each entity pair in a document. Evidence, defined as sentences containing clues for the relationship between an entity pair, has been shown to help DocRE systems focus on relevant texts, thus improving relation extraction. However, evidence retrieval (ER) in DocRE faces two major issues: high memory consumption and limited availability of annotations. This work aims at addressing these issues to improve the usage of ER in DocRE. First, we propose DREEAM, a memory-efficient approach that adopts evidence information as the supervisory signal, thereby guiding the attention modules of the DocRE system to assign high weights to evidence. Second, we propose a self-training strategy for DREEAM to learn ER from automatically-generated evidence on massive data without evidence annotations. Experimental results reveal that our approach exhibits state-of-the-art performance on the DocRED benchmark for both DocRE and ER. To the best of our knowledge, DREEAM is the first approach to employ ER self-training.