The trouble is that statistics are not raw data. Statistics is a method for analysing large data sets, raw or otherwise. There are plenty of ways of getting the statistics to say what you want. To start with, you could just make up the data. If you don't want to go for quite such blantant fraud, cherry-picking the data (or the subjects giving the data) and leading questions are always good. Once you have the data, there are many, many different ways of looking at it, so there's bound to be one that will lead to the answer you want.
For example, take some of the surveys on the Twin Towers, since this is a popular topic for manipulating the statistics. Let's say you want to show that the majority of American citizens think the government was responsible for this. Assuming it's a real poll and not just made up, the easiest way to get the correct answer is to pick the people you ask. Instead of randomly phoning people, go to a truther rally and ask your questions there. You're virtually guaranteed to get 100% thinking it was the government.
If you can't quite bring yourself to get that close to them, just pick your questions carefully. A good leading question would be something like:
Do you think the government could have done more to prevent the attacks?
With hindsight the answer is of course they could, and most people will answer something to that effect. The important thing is to have multiple choice answers such as:
a) No, they did everything possible.
b) Yes, security could have been a bit tighter.
c) Yes, the government is hopelessly incompetent.
d) Yes, the government did it on purpose.
e) Not sure.
Hardly anyone will pick a), which means you can proudly announce to the world that 84% of Americans think 9/11 was the governments fault, even though that's not what most of them actually meant.
The important thing with all statistics is that unless you can see the raw data, the collection method and the workings, it is all extremely untrustworthy and shouldn't be taken too seriously. Even with respectable polling companies, the questions are usually written, at least partially, by the people commissioning the poll. Polls just asking questions in the street, write-ins or, horror of horrors, online polls are essentially worthless. Statistics published in peer reviewed journals are likely to be better, and are at least open about the methods, but even then there are often arguments about the validity of the analysis used and possible biases in the population.
As with anything, don't believe something just because someone has written about it. Look for peer review, openness, replication and so on. Can you actually prove anything with statistics? Well, obviously not, since you can't prove something that isn't true. However, it's relatively easy to make it look like you've proved something to people who aren't skeptical enough.