The Transparency and Openness Promotion Guidelines (TOP) by Nosek et al. (2015) comprise a set of eight standards: citation, data transparency, analytical methods (code) transparency, research materials transparency, design and analysis transparency, preregistration of studies, preregistration of analysis plans, replication. Each standard has four levels that are increasingly stringent, ranging from 0 (standard not met) to 3 (standard fully met). For example, Analytical methods (code) transparency is rated 0 if the journal encourages code sharing or does not mention it at all, and 3 if code needs to be stored in a trusted repository and reproduced independently before publication. For further details, check the table summarizing the TOP guidelines.
The Reproducibility Enhancement Principles (REP) by Stodden et al. (2016) build on top of the aforementioned TOP guidelines and focus on computational research. The data, software, worflows, and details of the computational environment that is required to reproduce the results reported in the paper should be published in a trusted repository, including also negative results. Furthermore, the paper should link to these materials using persistent identifiers, e.g., digital object identifiers (DOIs). The recommendations also address the need to cite the materials underlying an article, to facilitate re-use using open licenses, and to check for reproducibility. Following these guidelines resembles level 2 or 3 of the TOP guidelines. For more details, check the article.
The FAIR Data principles by Wilkinson et al. (2016) provide a guideline to make data findable, accessible, interoperable, and re-usable. In short, (meta)data are findable if they have a globally unique identifier and metadata that are indexed and thus searchable. (Meta)data are accessible if they can be retrieved using a standardized and open communications protocol, and the metadata are accessible even if the data are no longer available. To be interoperable, the (meta)data needs to use a formal language for knowledge presentation. Finally, (meta)data are re-usable if they are released with a clear and accessible license, and the provenance of the data is known and described. Additional details can be found in the paper. If you would like to find out how FAIR your data is, you can simply check using the FAIR self assessment tool. Note: FAIR data are not necessarily Open Data. They can meet the requirements while being accessible only to a small group of researchers (see blogpost). Furthermore, the principles speak about (meta)data allowing data to become FAIR even if they cannot be published due to privacy/ethical concerns.