Requirements for naturalisation in Austria
Persons who want to become Austrian citizens have to meet the following standard requirements:
Continuous legal residence (basically ten years)
No ban on residence (Aufenthaltsverbot) and no pending procedure to revoke the leave to remain (Verfahren zur Aufenthaltsbeendigung) in Austria or any other EEA country as well as no issuing of an expulsion order (Ausweisung) within the past twelve months
Clear criminal record (no convictions and no pending criminal proceedings neither in Austria nor abroad, no serious administrative offences)
Proof of sufficient means of subsistence
Positive attitude towards the Republic of Austria
Renunciation of former nationality (if feasible and reasonable)
Knowledge of the democratic system and history of Austria and Vienna

Proof of German language skills (German)
If there is no legal claim to naturalisation other relevant factors are considered such as the standard requirements for naturalisation, the general public interest, the degree of integration and the overall conduct of the applicant (Art 11 of the Austrian Citizenship Act (StbG) - German).
Children (including adoptive children) of Austrian nationals who are younger than 14 years of agedo not have to prove German language skills and knowledge of history, do not need a proof of sufficient means of subsistence, and do not have to renounce their former nationality.
Children who were born on or after 1 August 2013 acquire Austrian nationality by descent, also if they were born out of wedlock and their father is an Austrian national if paternity has been acknowledged or established within eight weeks after the birth of the child.

Other ways of obtaining citizenship
Naturalisation due to a legal claim
Obtaining Austrian citizenship by extension - In certain cases, Austrian citizenship may be extended to children, spouses, and civil partners.
Granting citizenship for extraordinary achievements (Art 10 (6) StbG)
Obtaining Austrian citizenship by declaration (for persons who have their residence in Austria or abroad). Former Austrian citizens who lost their citizenship before 9 May 1945 due to racist and/or political persecution can reacquire their Austrian citizenship by declaration. They do not have to prove sufficient means of subsistence, German language skills, and knowledge of the democratic system and history of Austria and Vienna (Art 58c StbG).
Please contact a case officer for individual advice regarding the requirements for naturalisation in Austria: 

Citizenship test
The Austrian Citizenship Act outlines that persons who want to become Austrian citizens have to meet certain standard requirements such as knowledge of the democratic system and history of Austria and the province where the applicant has her/his primary residence. Applicants who are younger than 14 years of age do not have to prove knowledge of history.
Applicants will receive the learning materials for the other part of the citizenship test when they fix a date for the test. The learning materials provided by the federal government are available fordownload from the website of the Austrian Federal Ministry for Europe, Integration and Foreign Affairs. The Austrian Federal Ministry of the Interior is responsible for the contents of the learning material.

/www.wien.gv.at/english/administration/civilstatus/citizenship/requirements.html