It is some 16 years since I did the tests, we didn't know what to expect or have samples to try out before hand. Knowing however that we would be doing paper and pencil tests I spent hours and hours doing the types of tests that MENSA give you plus lots of logic type problems crosswords etc. They get your brain thinking quickly in a certain way.
Although you need to do some prep for them what they are looking for is your type of reasoning, no amount of cramming will really change the way your brain works so don't get yourself so uptight about the tests.