Hmm, no experience of this (live in the US, but public schools, so no private school knowledge).
From IQ tests, they'll test things like how you work things out, logic, common sense (although not so much this) etc; I think when DD3 did one once (she's 8, but was 7 then) one of the questions was somehting like this-
A blind man has a box with all his socks in. There are four pairs of socks per colour, and there are three colours- red, (can't remember so-) yellow, (can't remember so-) and green. He wants to get one pair of red socks out. What's the smallest amount of socks he needs to be certain he has one pair of red socks?
That was basically the question (can't remember exact wording) but then they expect the child to work out that that means there are twelve socks in total. They had to work out that you need to pull out nine pairs (I think this was quite hard for 7yr olds, or older children!)
Basically pretty stupid questions. Some are mathsy questions, a lot of them are things like 'If Amy's dad is three times Amy's age, and when you add the ages together, it makes one hundred-and-four when doubled, how old is Amy?' meaning they half one hundred and four, then divide by four, to get Amy's age. Weird things like that.
However, that's likely to be for your 8yr old, don't have a clue about a 4yr old!
Maybe you could, if you do want to have a go, have a try at riddles. It's a fun thing to do for them, it can help with IQ-y questions (I don't get IQ tests, no measure of intelligence) but really it's just fun. There are loads of simpler ones and some funner ones too, the problem solving ones are best, not just the 'what am I?' ones.
We are set to move to Houston in the summer 2013 and have a few private schools in mind. We're applying to 3 (deadlines mid Jan) and 2 have asked that we send through test results for WPPSI (4 year old!) and WISC IV (8 year old who will enter grade 3).
Fortunately DDs' school has an Ed Psy who can administer the tests but I have no idea what the tests contain. I gather they are more IQ rather than knowledge based but the questions themselves seem to be top secret. I obviously can't prepare my kids in a revision sense but just wanted to find out the types of things these tests cover. Anyone have any experience?