There are two databases which are used for bibliometric analysis. These are Web of Science and Scopus.
Web of Science
Web of Science is a citation database which contains bibliographic data to research publications. It contains references to Technology and Natural Sciences. Even Journal Citation Report is included in Web of Science. It can be used to check a journal's impact factor. There is also some tools built-in for bibliometric analysis. These can be used for some more simple analysis.
You can search the author's name and in the result list to the right you see Analyze Results and Create Citation Report.
If you click on Create Citation Report you get tables which show how many results where found, how many citations there are to the publications and even how many citations there are without self-citations. The difference between the total number of citations and number of self-citations is often very interesting to look at. It is better to have as few self-citations as possible.
Scopus is also a citations database but you have access to fulltext documents in the database.
If you have search for e.g. author then you can in the result list click on the author name to get results for exact the author you want. In the example below I have searched for Teherzadeh, M* but there can be a number of other author with the same name, I have clicked on Taherzadeh, M.J. When you do this you come to the author's page in Scopus where you can find many interesting things. If you click on View Author Evaluation you can find e.g. which journal the author has published most in.