How could I make my own reference (bibtex or other) to some arbitrary weblink like http://www.inf.ed.ac.uk/teaching/courses/anlp/slides/anlp13.pdf so that it appears under the 'References' of the PDF file generated by LaTeX.
However, whether or not and how the URL is displayed depends on your used reference style.
I had not realized that you didn't know there's a url field in many bibstyles. The four basic bibstyles (plain, unsrt, abbrev, alpha) are too old for URLs. More modern styles, like the ones provided by natbib(plainnat, unsrtnat, alphanat), and many others (e.g. ieeetrans and the ones created by custum-bib), provide a url BibTeX field.
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