The medicare levy is (generally) calculated as 1.5% of your taxable income, in certain situations you may have to pay the medicare levy surcharge also. You can find more information about this here.
That said, many taxpayers are not eligible for medicare benefits, and are therefore not required to pay the medicare levy. The medicare levy is included in an Income Tax Return by default, so if you are exempt from having to pay it, you must include a medicare levy exemption in that Income Tax Return.
Whilst it can be a fairly simple process to acquire a medicare levy exemption certification, it does take some doing, and can take some time. If you are eligible, then it is absolutely worthwhile, because it will increase your tax refund by 1.5% (in some cases more) of your total taxable income for that year. So if you have earned $50,000 - then that's $750.
To clarify a few points, firstly you need to be sure that you are not eligible for medicare, and secondly you need to apply to medicare for your medicare levy exemption certification, and wait until you receive it before you can lodge your Income Tax Return.
Most people seeking a medicare levy exemption certification are foreign residents, working in Australia on a short to mid-term basis. Employees working under a 457 visa are eligible for a medicare levy exemption, as they are not entitled to benefits. A frequent source of confusion comes from residents of United Kingdom, Northern Ireland,Italy, Malta, Sweden, the Netherlands, Finland or Norway. Australia has a reciprocal medical agreement with these countries which means that residents of those countries are not entitled to a medicare levy exemption. So even though you may not have registered for for medicare benefits during your time in Australia, you are still not eligible for an exemption.
If you lodge your Income Tax Return before receiving your medicare levy exemption certification, there is a chance that your tax return will be amended prior to your receiving your tax refund, and you will end up paying the medicare levy anyway. Processing your application for a medicare levy exemption certification can take some time. Generally it takes around four weeks, but personally I have seen applications take up to two months to be processed. Whilst the exemptions can not be processed until after the end of the financial year which they are for, it is a good idea to post of your application for medicare levy exemption certification a week or so before the end of the financial year, just to be sure that your application is at the top of the pile.
Now, preparing the application form is fairly straight forward, you can obtain the form here. The questions asked are fairly straight forward. Probably the trickier part is providing the additional documentation required. You need to provide certified copies of every used page in your passport. So you need to photocopy every page, up to and including the last used page in your passport, even if there are pages before that last used page which have no stamps or visas there-on. If you entered Australia on a prior passport, then you will need copies of that passport too. Then you can simply present the copies and the original to an authorized person (there's a list on the medicare website).
I have seen situations where a taxpayer entered Australia on a prior passport, which has since been destroyed, in such cases you will need to apply to the Department of Immigration, for your entry and exit records, and then submit those to medicare with your medicare levy exemption application.