The means for doing this are too varied to allow specific instructions, but some general comments may be helpful. Before you begin downloading, make sure you have marked what you want to copy, if this is appropriate.
Some databases have options to select individual citations, for example.
Or, in a frames environment, you may have to select a single frame. Also, be sure the information is in the form you want. Some full text databases, for example, allow you to switch between text and brief citation. If you have only citations showing, you will not get the full text when you download. Or, if the file is a simple one in HTML, you may be able to email it to yourself using this feature of the browser.