If it is mandatory to do something mainly depends on citizenship, gender and age, and it is relevant to both minors and adults. But even if, this "something" does not have to be military.
First, some short facts:
- If you're planning to live in Austria without acquiring Austrian citizenship, you don't need to worry about anything. It's both unnecessary and impossible to participate in all of the following things.
- The mandatory parts here are only relevant for males (just in case: biological males according to a doctor). Women can participate voluntarily, but don't have to.
- If someone with Austrian citizenship acquires a different citizenship and loses the Austrian one at the same time, he/she can forget about it too, independent if a part of the process below was already done or not.
- In case of multiple citizenships, it depends. When in doubt, see (or call) the next base with a "Stellungskommissionen" or a lawyer.
- While holding Austrian citizenship, any form of voluntary military service in another country leads to losing said sitizenship.
For male Austrian citizens, following steps are mandatory. Failure to comply, even after they forcefully pick you up at home, can lead to prison (up to one year). For all parts, being able to speak German is very helpful (They have courses too, but the expected progress speed is pretty harsh.)
Part 1: Musterung / Examination
All males have to undergo a two-day examination at a military base.
Normally, this happens between the 17. and 18. birthday. A letter with details, including date and place, will be sent some months before. Reasons like eg. being sick at this date is a valid excuse to move the date (but not multiple times).
In case someone got Austrian citizenship after the 18. but before the 35. birthday, it still can happen (or you get off easy, if they think they have enough people already). If the citizenship is acquired after the 35. birthday, you can just forget it, nothing happens anymore.
People with Austrian citizenship, but living abroad permanently, will get the letter as soon as the move back to Austria (if they do, and if it is before their 35. birthday).
Bed and food will be provided, as well as compensation for bus/train tickets if shown.
The examination itself contains medical (eyes, ears, blood test, ECG, ...) and psychological (questionare and talk with a psychologist) parts, as well as tests of arm and leg strength, reaction speed, ability to differ between targets, etc. It is strongly advised to come "clean" of pretty much anything (eg. one week prison because showing up drunk happens). If you have glasses, or anything else relevant to health, take them with you.
At the end, you'll either pass ("tauglich") or not ("untauglich"). With some temporary disability like a cast, it also could be that they want to see you again at a later date.
If being "untauglich" / failed, the whole procedure is over. Otherwise, you have the possibiliy to specify on a form (now, or later per post) what kind of service you want: See below.
Part 2: Basic Service itself
Soon after the examination (but not before the 18. birthday), the people who passed get another letter when they should start their selected variant.
Things like finishing a school year are valid delay reasons (as long as they are communicated properly). Not living in Austria is no excuse this time; if you were at the examination you're expected to come for this part too.
a) Military
Basically 6 month of basic training. Between monday and friday, being at the assigned base is mandatory (bed and food etc. provided again), saturday and sunday can bei either at home or at the base.
There is a (very small) monthly salary of ca. 310€: it's expected that you don't need to pay rent for something etc. because you still live with your parents, and food etc. during the week is free. A nice perk is that some (not all) can get a driving license paid by the military.
Unless you choose to stay (extended training, officer / specialist training, permanent employment), it's over after this 6 months.
b) Community service ("Zivildienst")
If you signed up for this instead, you have to work at eg. hospitals / ambulance, elderly care etc. (there's a specific list what kind of institutions are allowed, most of them are in the mentioned areas). Unlike the 6 month of variant 2a above, this is 9 or 12 months (depending on the kind of job), usually no bed and food but still the same small salary, no free driving license, ... yeah, they don't want too much people choosing it.
What you need to know for the job is taught by the institution. There are both office and practical jobs, latter range from eg. ambulance car staff down to things like cleaning, cooking and gardening. Another note: Going this path, a job at the police becomes impossible.
Part 3: In case of a war etc.
If the full-time part and the current basic service soldiers are not enough for something, people who did variant 2a can be drafted anytime, until the age of 50. For some specialist roles, it's up to 65.
Disclaimer: I'm not a lawyer.
Sources (not the easiest, but most complete ones):
Wehrgesetz
Zivildienstgesetz