If you don't want to claim a tax deduction for your contributions to your super fund then all you need to do if find out from your fund the account details or BPay details for you to make a contribution. As this would be going into your super fund as after tax dollars they are not taxed within your super fund at all.
If on the other hand you wanted to claim a tax deduction for the contributions you would need to contact your super fund after the end of financial year and tell them how much of your contributions for the year you want to claim a tax deduction for (they would have a standard form on their website to do this). Then once you receive confirmation from the super fund that they received your notification to claim a deduction on your contributions, you can then do your Tax Return and claim the deduction for your super contribution in your Tax Return. The amount you claim a deduction for in Your Tax Return will then be taxed at 15% in your super fund.
However, if you do not need to file a tax return in Australia, or you have earned below the $18,200 tax free threshold, or you are getting any tax paid during the year fully back, then there is no need to claim a deduction for your super contributions as you would not be needing to use it and you will just end up paying the 15% tax in your super fund.