While it’d be nice if you could expect to go up exactly 2400-p points (where p = your starting score), it’s a good idea to have more tempered expectations as you begin your SAT prep journey. What follow are some generalizations based on my experience. Your mileage may vary.

• Improvement is relative. If a course or tutor claims an overall average improvement (“our students improve 200 points on average”), keep in mind that figure doesn’t take into account the starting scores of the students. It’s a lot easier to bring a 1500 to a 1700 than it is to bring a 1700 to a 1900. It’s even harder, of course, to bring a 2100 to a 2300. A 200 point improvement is a great goal if you’re starting around 1700. It might be less realistic (though not impossible) if you’re starting at 2000.
• Improvement takes time. I like about 2 months of regular prep before the exam, but I’ve worked with lots of kids whose improvements have taken longer. If you start your prep 3 weeks before your test, you’ll probably be disappointed in your improvement.
• Improvement depends a lot on what you already know. One of the best ways to improve your math score is to get into the habit of working with real numbers instead of variables whenever possible. This is the first thing most tutors and courses will teach you. If you’ve already been doing that on your own, then obviously you’ll see less benefit from that technique than someone who’d never thought to try it before. The same can be said of studying vocabulary. If your vocabulary is awful when you start, and then you learn a ton of words, you’ll probably see a nice reading improvement from that alone. If your vocabulary is already really good, then it’s still a good idea to learn as many new words as you can, but it’s going to help your score less.
• It’s easier to improve in some sections than it is in others. The writing section (the multiple choice section of it, anyway) tests you on mostly straightforward rules, so once you nail them down, (especially if you didn’t know what to look for before) you should see a HUGE improvement there. Some of the hardest math questions are susceptible to a few simple techniques, but the SAT will also throw some really difficult questions at you that those techniques won’t help you with, so you might see a nice initial score jump followed by a plateau that’s hard to overcome. The reading comprehension section follows patterns too, but they’re much more difficult to learn, so large improvements there will require the most dogged persistence. Expect your reading score to improve slowly.
• All that having been said, it doesn’t take a miracle to raise a score. A good rule of thumb is this: one fewer mistake per section should add about 100 points to your score.  See for yourself if you’ve got a scoring table handy from a test you recently took. Changing one answer from wrong to right in each multiple choice section will add 3.75 raw score points to your reading and math scores, and 2.5 raw score points to your writing score. For example, if you scored 650 in each subject on the first test in the Blue Book, adding those points would get you: 690 reading, 680 math, and 690 writing (assuming an essay score of 8). You went from 1950 to 2060. Not bad, eh?