How to make the ASTB your bitch
+1 to what CaliFlyer said. Both books are good; I studied from both and took all the ASTB practice tests in those two books. The gouge on here is also very helpful. With those two study guides, the gouge on this site and some focused study time I scored 8/8/8 57 even though my girlfriend thinks I am partially retarded. For what its worth here are some pointers to help you study for each specific portion:
Math: If you can do the math at the pace required to answer all questions in the practice tests when timed you will find the ASTB math to be easy. I felt the math on the actual ASTB to be simple in comparison, but the books were good prep because they were more difficult. There is nothing higher than basic algebra, just know the basics well and practice for speed.
Verbal: The ASTB is all paragraph comp, so don't worry too much about memorizing a dictionary to learn new words. If you get one of the paragraphs that are describing a complex situation, draw a picture or map, I found that very helpful. If all you have ever read is Calvin and Hobbs and Cliff Notes this section may give you Hell, but if you've read a couple books throughout college or enjoy reading on your own, this section is no biggy. I felt this section leaves you plenty of time to read each paragraph, just practice the paragraphs in the test books to get an idea of the pace.
Mechanical Comp: The study books and gouge are great prep for this section. If you read over that stuff and have a little common sense you should find this section pretty easy. I might have just lucked out, but I do not remember getting a single question in this section that required calculating a specific number to find the answer.
Spatial: Practice these from all of the available gouge and study guides until you feel airsick. The more you practice these, the easier they get. Note that in the real ASTB there are no clouds, two levels of bank (shallow and steep) and the airplane is difficult to make out, but if you have practiced from all the guides, learned to pace yourself and use the process of elimination to narrow down your choices you can rock at this section even if you have never been in an airplane before. If you have a flight-sim on your PC or can get up for a flight lesson this may help you understand what the horizon does as you put a plane in different attitudes if you are new to aviation.
Aviation/Naval info: The aviation and naval knowledge in the two study books was plenty of info to do well on the ASTB, but the more books you study from the better if you have time or limited flight experience, just don't get too worked up over the aviation/naval sections, they are all very basic questions.
Aviation Supplement: This section combines identical or similar questions from the above sections. Study the sections above and you will be prepared for this section. Keep an eye out for questions you may have already answered in previous sections. I think they might be testing your short term memory a bit by putting in some questions you have already answered on the test so lay off the bong Cheech. I think they might be testing your short term memory a bit by putting in some questions you have already answered on the test so lay off the bong Cheech. Hopefully you got the identical ones right the first time around.
Extra tips for test day: Sleep well, eat well, hydrate, and get some exercise in the day before to help get out some of your tension. If they give you the option, take your PRT before your ASTB in the event you end up doing both on the same day. Taking the PRT first will help get out more of your nervous energy, get blood flowing to your brain and allow you to focus better. During the break you get while taking the real ASTB get up, hit the head, and move around. Anyone can do well on the ASTB if they apply themselves. Focus on any weaknesses to make them your strengths and you will be walking out of the test that much closer to your dream.
Good Luck on your ASTB!