To fetch entries from an online database, choose View → Web search, and the search interface will appear in the side pane. Select the database you want to search (e.g. arXiv) in the dropdown menu. Enter the words of your query, and press Enter or the Search button. The results are displayed in the import inspection dialog.
Some of the databases support advanced search queries. These are described on the detail page of the database.
Apart from fetching entries by using a full search it is also possible to directly create an entry using a unique identifier.
JabRef is not intended to be a tool for mass download of citations. The purpose of the Web search is to easily gather a few entries directly from within JabRef. If you use the search functionality to extensiviely you might get blocked (for some time).
However, it is still possible to import hundreds or even thousands of entries from these databases. The process depends a bit on the specifics of each database, but in general works as follows: Search the database in your browser, export the result in one of the supported file formats and then import the file into JabRef.
If you need to use an HTTP proxy server, you can configure JabRef to use a proxy using the "Network" preferences (Options → Preferences → Network).