If you or your spouse are austrians, then you can apply for a family residence permit, you can find all the info in the same place as the regular residence permits.
Officially the austrian national will be sponsoring the parent (or parent in law), you have to prove additionally that you have enough resources to support the new person, usually it is 1500 EUR monthly per sponsored person.
Also that your parent is dependant on you, for instance you can show previous statements of wired money, plus the regular docs: employment, salaries, debts.
After you have all the documents, you send them to your parent and he/she has to go to the local austrian embassy in the country of residence and then it takes around six months more or less to get an answer.
If the answer is positive then the parent will be getting a temporary visa to enter Austria and once here s/he will get the residence permit that needs to be renewed every year and without any access to the labor market. You also have to pay additionally the WGKK before getting the residence.
If no one in the couple is austrian, I am not sure but I think it is subject to quotas...
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