It's important to realize what you are doing in an assumption question.
Consider the following argument:
Mike is the best deer hunter in New York City. There will be a deer hunting competition in New York City on Friday next week. Since Mike is the best deer hunter in New York City, he will surely win the competition.
Although this argument seems quite simple and logical, there are so many assumptions underlying it.
For example, the author has assumed that Mike will attend the competition. How can Mike if he does not attend? The author has also assumed that the competition will only contain people from New York City (what if Carl, the best hunter from New Jersey, attends the competition? Is Mike sure to win then?) or alternatively, that Mike is better than anyone else attending the competition. The author has assumed that the deer hunting competition will be judged on deer hunting -> What if the judges are corrupt?
The list goes on and on. There are infinitely many assumptions packed into this tiny argument.
An example answer choice to this passage would be:
A) Mike is in New York City on Friday, and will attend the competition.
This might be for an easier level question, where it is easy to see how it links to the assumption.
A harder level question might have something like:
A) Mike recently went to the doctor, and the doctor has assured him that he will not be ill in the following week.
This also relates to the assumption of Mike attending the competition, since if he is ill he will not be able to attend. But this is much more "roundabout" than the first version.
Knowing the above, then it is clear that while doing GMAT/LSAT assumption questions, your task is to find "what is unstated". You need to find where the author makes "jumps" in the reasoning. Obviously, you do not have time to list every single assumption of an argument, since there can really be infinitely many, however it is good practice to pick a question, and write down all the assumptions so you can train yourself to spot them. Assumptions can be big or small, and there is really no limit.
A good technique to learn is the negation technique.
You can invert the answer choices, and see how they impact the argument.
In our silly example, suppose we inverted the easy version of A:
Mike is in New York City on Friday, and he will attend the competition -> Mike is NOT in New York City on Friday and he will NOT attend the competition.
It becomes clear, that through the negation technique, that if A is somehow false, then the authors argument falls apart (If Mike does not attend, there is no way for him to win).
It also works for the harder version:
Mike recently went to the doctor, and the doctor has assured him that he will not be ill in the following week -> Mike recently went to the doctor, and the doctor has assured him that he WILL be ill in the following week.
Negating the hard version, it also becomes clear that it is an important assumption. If Mike is sick, there is a good chance he will not attend the concert and thus not be able to win.
In essence, to get better at assumption questions you will want to:
1) Understand what an assumption is, and how to spot them in passages
2) Learn how to apply the negation technique, so that you can be certain of your answer choice. The negation technique, at high level questions, can become quite tricky to apply, so it is important to practice.
Hope this helps!