I just took the ASTB today for the first (and last) time and scored a 69 9/9/9. I studied a little bit at a time with the ASTB Prep app over the last couple months, but wasn't able to do as much as I planned due to final exams. I found the ASTB Prep app to be very helpful,
especially for terrain identification and UAV, but there are many different things that can be on the test, so the app doesn't cover everything. It is great for the general things you need to know though. I also studied some of the mechanical stuff with the videos linked by user mattdavid123 on post #5129. I studied for a couple hours a day the last few days to brush up on math, ANIT, and mechanical comprehension concepts. I used the cram flashcards, but could never get through all of them. I also practiced with an X52 using the remade jantzen sim:
https://jomo1-1.github.io/ASTB-remade/
General Advice:
Do not worry if the questions seem harder than expected. That is a good thing and means you are doing well. The key is to stay focused and keep working and do not panic. I got cut off for time on the math and reading sections, so I think correct answers may hold more weight than speed, but you still want to get through as much as possible.
Math:
KNOW ALGEBRA WELL
You should be able to add, subtract, multiply and divide any numbers relatively quickly.
The geometry concepts were less involved and mostly were about finding areas. I did not find any need to use the formula tab. I ended up getting a lot of logarithm questions, but no matrices. You should know how to convert between exponential and logarithm form and have a good understanding of exponents, specifically exponents with fractions ex. x^(3/4).
Reading:
There is really nothing to note here studying-wise because it is just reading. The passages were very boring and were all related to naval procedures and instructions, but you wouldn't need to know any naval jargon. It is difficult to stay engaged and focused in this section because of the way the passages are, but you just have to keep working and choose the answer that is most consistent with what is in the paragraph.
Mechanical Comprehension:
Most of these questions are purely conceptual, so it is important to know the concepts behind things like flow rate, particle motion, momentum, simple machines, etc. Solving problems will help understand these concepts, but knowing the relations between variables and having a general understanding of physics concepts is sufficient.
ANIT:
This section is tough because there are so many things that can be on it. Some things you definitely need to know of course like which control surfaces control what motion over which axes because you are pretty much guaranteed to have questions on this. There were a couple questions on parts of a ship. There were definitely questions that were covered on the cram flashcards, so if you can go through those, it would be helpful.
NAFTI:
As others have said, just pick the option that you think best describes you. Definitely a weird section because it feels like the answer choices aren't really relevant to each other and there is no right answer.
PBM:
If you can get a stick and throttle setup to practice, do it, but I don't think it is necessary to do well. I did not find dichotic listening to be very difficult, but I did make a couple mistakes during the part with all 3 (stick, throttle, and listening). I don't think I am particularly outstanding when it comes to tracking the targets with the stick and throttle, so just do the best that you can and try to do well on the emergency procedures and listening parts. For UAV and terrain identification parts I will deviate from what others have said. Practice with the ASTB prep until you can get the right answer quickly pretty much every time. There is no need to use the pencil/compass trick for these sections as I feel that it just takes up extra time. Just practice it until you understand it well.
Lastly, thanks to everyone on here for posting your resources and strategy as it has been very helpful.