Data preparation, also called data wrangling, is considered one of the most expensive and time-consuming steps when performing analytics or building machine learning models. Preparing data typically involves collecting and merging data from complex heterogeneous, and often large-scale data sources, such as data lakes. In this paper, we introduce a novel approach toward automatic data wrangling in an attempt to alleviate the effort of end-users, e.g. data analysts, in structuring dynamic views from data lakes in the form of tabular data. We aim to address table augmentation tasks, including row/column population and data imputation. Given a corpus of tables, we propose a retrieval augmented self-trained transformer model. Our self-learning strategy consists in randomly ablating tables from the corpus and training the retrieval-based model to reconstruct the original values or headers given the partial tables as input. We adopt this strategy to first train the dense neural retrieval model encoding table-parts to vectors, and then the end-to-end model trained to perform table augmentation tasks. We test on EntiTables, the standard benchmark for table augmentation, as well as introduce a new benchmark to advance further research: WebTables. Our model consistently and substantially outperforms both supervised statistical methods and the current state-of-the-art transformer-based models.