Data are available publicly on several websites e.g. icpsr, databank, UK Data Archive. I am seeking guidelines, references and examples about using these open data for research. In other words, I want to publish a paper based on analyzing some publicly available datasets. Do I need permission first or they are available actually for me to use them in my research ?
A public data set is just that: public. They have been made available for the specific purpose of being used by other people.
Thus, you generally do not need permission, but you will need to appropriately cite the source of the dataset, thereby giving appropriate credit to its originators. For a well-curated collection, you can find appropriate citation information embedded within either the "packaging" or metadata of the dataset or at the online source where you obtain it.