I took mine six months ago (and due to go back). Went to Vision Express and they did a very thorough test - first looked in a machine where they measured the eyeball and got a prescription estimate, then an eye test with the optician using pictures rather than letters.
My HV recommends all children at the age of 3 start going for regular eye checks (something I think is probably right - my short-sightedness got missed for a good while as a child). She also mentioned that one of the signs of short-sightedness is a child who blinks a lot (as they are trying to "clear" their eyes to see better).
My ds1 (3yrs 8mths) is very slightly short-sighted but not bad enough for glasses yet. Was told to take him back after six months (and I really must make that appointment!)