When selecting a method of data sharing, there are several things to think about:
The ideal data-sharing solution makes it straightforward for interested parties to find out about the data and acquire a copy. It will ensure that the data remains available long into the future.
Whichever method is adopted, it is good practice for research publications that use the data to include a data availability statement. This is a brief note that either indicates where and how the relevant data can be accessed or, if some or all of the data is not available, explains why this is.
One of the best methods of making data available for reuse is to deposit a copy in a specialist archive or repository. Archives exist for the specific purpose of preserving and sharing data, and as such, they are well-equipped to make data discoverable, accessible, and sustainable.
IZTECH has its own institutional repository for research outputs, including datasets. Also, APERTA is an open archive in which all Turkish Researcher can share their data.
You can check the Re3data for extensive catalogs of data archives.
Many data archives can apply access controls to data deposits and hence may be a good option for data that is not suitable for completely open sharing.
If your research project has a website, it may be appropriate to host a copy of the data there. This can be an effective way of sharing the data with a wider public and may allow you to offer features that would not be available via a data archive, such as a custom search interface.
However, it is not advisable to rely on this as the sole method of making data available for the long term. Maintaining a website after a project concludes presents several challenges: funding bodies are generally reluctant to cover costs incurred after the end of the grant period, and project team members are likely to move on to other endeavors, and hence it is hard to predict how long a project website will remain viable for. If possible, a project website should therefore be seen as an additional method of sharing data alongside depositing a copy in an archive rather than as an alternative to it.
Several services exist to make it easy to share research material (including but not limited to data) online. These may be publicly-funded services or commercial ones and include Zenodo and the main Figshare service.
These platforms vary a good deal, so it's important to check the terms and conditions carefully. They can provide a quick and convenient way of making data and other materials available, but data may not be as easily discoverable, and sustainability is not always guaranteed. They are also generally less likely to offer active curation of data or access controls than specialist repositories or institutional services.
In some fields, researchers may provide data files to be published alongside the journal article, which presents the conclusions drawn from the data. This makes it easy for readers to access the data and has the advantage of presenting it in context. If the journal is a well-established one, it is also likely that the data will remain available for a considerable period (though it is worth checking the journal terms and conditions to see whether this is guaranteed).
However, there are once again reasons not to rely on this as the sole method of data sharing. While making the data available this way is convenient for readers; it may be harder for other interested parties to discover the data. Additionally, the data relevant to a particular article will frequently only be a subset of the data produced by a research project. Where possible, it is, therefore, a good practice to also deposit a fuller version of the dataset in a suitable archive.