I've read about 100 different posts on the POSS and how it may or may not be graded, calculated, tabulated, stipulated, or anything else :p But I can tell you how it works at VC Summer since I just took it...
(in the order we had to take the sections)
Math: 46 problems, 13 minutes; conversions, short algebra, word problems
The test giver told us that wrong answers in this section count against you, and that your total correct number (correct - missed) will be multiplied by 2. I think she said something like you only need 10 correct in this section. I probably got 36 or so... the time is insane on this one. If you can complete this section in the allotted time, you probably need to go design rockets. The questions are not hard, the timing is. I left the word problems for last because they suck. Recommend doing the easy conversions, the easy algebra, the harder conversions, the harder algebra, then moving to word.
Assembly: 20 problems, 10 minutes
Wrong answers do NOT count against you on this section, and the total correct is multiplied by 4 (as opposed to 2 in the math section) because it is considered the most difficult section. I didn't get to 1/20 of them... doh. I will say that many of them were more difficult than the practice test. How exactly I cannot say, I think mainly that the answer selections were more similar than dissimilar so it took longer to narrow down the correct one.
Mechanical Reasoning: 40 questions, 20 minutes (I think)
She didn't say about the multiplier or whether these count against you, but I am assuming incorrect answers do. You cannot really study for this, its either junk you can or cannot solve based on simple physics, life, mechanical knowledge, or imbued brilliance.

. I will say there was one mechanical one I just couldn't figure out... because the drawing was confusing. It looked like a 4 year old etched two leavers and a blob in between :p
Tables: 60 questions, 5 minutes (I think it was 5)
I answered them all (most likely correctly). I think these count 1 point each and wrong answers do hurt you. However, if you are a fast table reader, this gets you "freebie" points. Such an easy section in my opinion.
Graphs: 20 questions, 3 minutes (I think...)
Same thing as above, takes a bit longer to derive answers because they lines are all the same frickin color and width so even when you find the line on the graph, you have to trace it back to the letter. Most graphs aren't like that in the real world...
Reading comp: 36 questions, 30 minutes or so
If you can read the newspaper, you can do this. Pretty sure there were 5 articles and about 6-8 questions on each. I finished 10 minutes early, but your success on this test will probably be a function of your reading speed. Make sure you read the choices carefully, some of them are a "trick" (like inverting the wording on something you just read which inverts the answer in some cases).
The employer tallies up your total scores on all COMBINED sections, and if you fall within a certain range for operations, you pass. She didn't say what that was. She did say ops had to get higher than some other jobs. I should find out later today how I did, optimistic for now :p