There isn't one exact approach that will work for everybody—our brains work differently and so we have to adjust approaches accordingly. You said that you feel that not knowing the premises by heart is resulting in a disadvantage for you on certain question types, and so we need to figure out some better approach for you with those question types.
When you say that not knowing the premises "by heart" is putting you at a major disadvantage, does that mean that you are finding yourself falling for traps (or just not seeing the right answer) because there is some particular detail in the premise that you have forgotten to consider? I'm guessing it's something like that.
For Assumption Family questions (Assump, Str, Weak—the ones you name), the primary issue typically lies between the premises and the conclusion—in the underlying (and unstated) assumptions that allow the author to make the leap from his/her premises to his/her conclusion. So, yes, on these question types, it is important to note the premises as well as the conclusion—ie, the overall flow of the argument as a whole.
Also, just a note. You talked about attacking the premises. The premises themselves are given—we're supposed to accept them as true. What the answers are really attacking are the assumptions that lie *between* the premises and the conclusion. And, yes, those of us who are really good at this test have learned how to brainstorm the unstated assumptions that lie in between. Here's a (relatively straightforward) example:
Revenues of product X went up last quarter, so profits for product X must also have increased.
Unstated: Assuming that...costs didn't go up enough to cancel out those revenue gains.
No mention is made of costs, but obviously costs factor into profits—so you can't conclude that profits went up just by knowing that revenues went up.
Some arguments are shorter and more straightforward. For those, you might be able to keep both the premises and conclusion in your brain as you look at each answer choice. (And those also might feel like the correct answer is just attacking the conclusion, because the correct answer is so closely tied to the conclusion.) For these, I would pause just to make sure that I've got the sequence straight in my head, yes.
Other arguments, though, are longer or more convoluted—for those, the unstated assumptions might not be so clear. Here, you're going to want to jot down a little "Map" of the argument (premises + conclusion = argument) so that you can understand the flow of the argument. That will help you to identify the unstated assumption that might be at the heart of the correct answer. (And this is essentially a longer version of the pause I mentioned in the previous paragraph.)
When making a Map:
(1) Do not just copy down the argument as it is written.
(2) Instead, look to put things into your own words—that means you actually understand the "story" that the argument is telling. (Though if there are certain words that really matter, you can use the same word. For example, "most people" has a different meaning than "lots of people" or "many people." If the argument says most, you should probably write down that exact word.)
(3) Also, abbreviate heavily and develop your own "vocabulary" of abbreviations. People = ppl. City council = CC. Use symbols. --> means the first thing leads to or results in the second thing (cause and effect). Use > and < to mean more than / greater than and less than. Use up and down arrows to indicate that something is increasing or decreasing. And so on. You can abbreviate however you like; you just want to practice it so that you can develop certain symbols / patterns in advance. That's how you get really efficient with it.
Next, let's talk about how you can train yourself to start to spot the unstated assumptions. Go back to CR questions that you've done recently. Articulate this to yourself:
1) The premises
2) The correct answer
3) The conclusion
Now, look at how the correct answer fits into the "gap" between the premises and the conclusion. If it's an Assumption question, you should be able to say, "The author assumes that <the information in the correct answer> is true, even though the argument doesn't say so. And that assumption is filling a gap between the premises and the conclusion—you do actually have to assume that this is true in order to get to the conclusion."
Here's how that would work on my mini-argument about the revenues.
1) Revenues went up.
2) Costs did not go up so much as to offset the gain in revenue.
3) So profits must have gone up.
In this case, we know that R + C = P, so the assumption about the costs is necessary in order to draw the given conclusion. The correct answer does fill in this gap between the premises and the conclusion. (You can also try plugging in the wrong answers to see how they do NOT fill in the gap.)
If, on the other hand, the question is a Strengthen or Weaken, the evaluation is a little bit different. Rather than saying that the correct answer is
necessary to fill in the gap, you're going to say that the correct answer,
if true, makes the argument at least a little more likely to be valid (strengthen) or invalid (weaken)—but it's not actually necessary for this information to be true. You can still look at the same 1-2-3 sequence as noted above; just use this different way of evaluating.
Again, try this on some old CRs that you've already done to see how the correct answer does make the overall argument a little more or less likely to be valid. (And incorrect answers will fail this test.)
If you'd like more on any of this, you can find it in our Critical Reasoning Strategy Guide. Good luck with your studies!