Among the many ways in which journals differ in the way they expect authors to format references is the way names of journals are given-whether spelt out in full or abbreviated (Current Science versus Curr. Sci., for example). The abbreviations may also be different - journal being shortened to simply J or to Jnl - but, fortunately, are practically standardized now. This post offers some tips on dealing with the abbreviations.
Look up references in a recent issue of the target journal. In most cases, authors of papers published in your target journal will have already cited the journal title that you need to abbreviate. Examine a few published papers on the same topic published in the target journal to see if the journal title in question is listed and use the same abbreviation.
Look up the websites of abstracting and indexing services. Because abstracting and indexing services cover thousands of journals and typically abbreviate their names, websites of Chemical Abstracts (publishers of CASSI, or the Chemical Abstracts Service Source Index)  and BIOSIS (BIOSIS Serial Sources) are likely to include the journal title you are looking for.
Another comprehensive source is ‘All That JAS', or Journal Abbreviation Sources , which points visitors to Internet resources, organized by disciplines (from Agriculture and Anthropology to Religion and Veterinary Medicine) that provide full titles of journals and abbreviations of those titles.
Abbreviate the title from the standard abbreviations of its constituent words. If you wish to abbreviate Malaysian Journal of Oncology, for example, and cannot find the title, you can build up the abbreviation using Malay. for Malaysian, J. for journal, and Oncol. for Oncology because this is how these words are abbreviated according to ISSN. Standard abbreviations for common words are available at the ISSN website: http://www.issn.org/2-22661-LTWA-online.php.
Do not abbreviate single-word titles. Names of journals that run to only one word - Nature and Science, to cite two famous examples - are not abbreviated.
Match the target journal's style for abbreviations. Journals differ in whether they end the abbreviated words with a dot, whether they print the abbreviated titles in italics, and whether they capitalize every significant word in the title. Examine the style used by your target journal and follow that.
["Publish and prosper" is a series of posts about tips for researchers whose first language is not English but who submit papers to journals published in English. The series touches upon not only writing (spelling, grammar, punctuation, usage, and style) but everything else relevant to publishing research papers that journal editors wish their authors knew.]