I don't have any specific situation on the situation in Austria, but in general there are a few things that you should keep in mind. First of all, the official website of the Austrian tax authorities appears to be this one: https://www.bmf.gv.at/steuern/startseite-steuern.html. There is an English page there, but it is mainly aimed at international businesses. The part about tax treaties may be relevant, though. The general procedure is outlined here: https://www.bmf.gv.at/steuern/startseite-steuern.html. Like I said in my comment, most information is likely only available in German. I would strongly advise to ask help from someone who speaks German and is familiar with the tax system in Austria.
The main thing that you would have to do first is to check of which country you are a resident for tax purposes. This is usually the country in which you lived for more than 183 days in the past year. If you moved during the year, and had income from more than one country, you may have to file tax returns in both countries. There are tax treaties between Austria and the UK (and most other countries), so you would have to check those treaties to find out what gets taxed where. In principle you get taxed only once, but usually you would have to declare all income.
The last important thing is of course to make sure you submit before the relevant deadlines.