Roughly half of the graded questions on the LSAT come from the two logical reasoning sections. Although the logic games often give people troubles and the reading comprehension section will normally have one extremely boring or frustrating passage, a lot of ground can be made in obtaining a higher score by practicing one simple method to answer logical reasoning questions.
1. Skim the question stem first
Knowing what the question is testing (flaw, strengthen/weaken, main principle, etc...) will greatly aid in focus while reading the passage above the question stem as well as helping your subconscious know what to look for.
2. Mentally rephrase every sentence
This seems tedious at first, but it is actually the key to doing well on logical reasoning questions. When practicing prior to the test rephrase each sentence in the passage aloud. For example if the passage were to say "In international diplomacy countries with populations under 6 million have more formal alliances than countries with larger populations." After reading that sentence I would quickly rephrase it into something like "smaller countries have more alliances than large ones." The key to rephrasing is to state the obvious so that it sticks in your brain. If you do this for every sentence in a 4 sentence passage (most passages in the logical reasoning have about 4-6 sentences, though they tend to be meaty) you'll understand the passage much better than if you had simply read it. This way you learn what you're reading while you read it.
3. Never, never, never re-read an answer choice before reading all answer choices
Many LSAT test takers struggle with this concept. They'll read answer choice A, be slightly confused and then re-read the answer choice, or, worse, look back to the passage to see if it is right. Do not waste time re-reading what is likely not the right answer choice (because of the way LSAT does things question A is right a little less than 20% of the time). If it seems confusing it is likely not right, especially if you've done the first two steps. Mark it if you think it may be right and come back to it after you've read through all the other choices. Often this approach helps students quickly narrow the answer choices down to two or three real options, of which A or B may be one, and then they can easily eliminate the wrong answer(s) in order to pick the correct choice.
These three simple steps can be hard to implement at first, but with practice they can be valuable tools in increasing your LSAT score. Considering the fact that approximately 50% of the test comes from logical reasoning questions it is worth it to implement a method like this one, and as an added bonus it actually applies well for many reading comprehension questions and from time to time is useful on logic games as well.