I would take the standard 5 paragraph Essay format but modified for brevity. Your thesis or introduction answer should be your immediate answer to a writing prompt and should be no more than one sentance. Rephrase the question as your sentance (i.e. if the question is "What would be the platform you would run on if you were running for President of the United States?" then your response should be "If I were to run for President of the United States, my platform would address [item 1], [Item 2], and [item 3]."). Your conclusion paragraph should restate the thesis. The three paragraphs in between should briefly address best arguements for your thesis in order of strongest to weakest (for me, my answers would be economic improvement by reworking tax laws, foreign policy that would place the country in step with a more neutral pre-WWII dealing, and an infrastructure modernization program.). A good 3-4 paragraph argument would suffice for each.
Now before I give you my last piece of advise, do keep in mind that this was given to me by a teacher at an all boys high school, so it was tailored to it's audience of teenager boys who naturally have only one thing on their mind at any give momement. It still helps me to this day, and the somewhat crass nature of the analogy hammers it in:
"A good essay should be like a girl's skirt: It should be long enough to cover everything but short enough to keep it interesting."
That is you shouldn't get far into the weeds on your point or points, especially on test essays. Also do not feel the need to hold strictly to the word count other than try to get the 250 word mark (most essays graders will judge by the eye, so a little wiggle room is allowed. Additionally most won't mark down if the essay goes over 250, though again, keep it close... they aren't asking for a Tolkien novel series. Obviously if you have a word counting program (assuming it's typed and not handwritten), don't short by a word and find a way you can squeeze in a fancy adjective that isn't going to be supferlous.
250 isn't a lot to work with. To get an idea, a 500 word essay assumes 5 paragraphs, each 3-4 sentances long and will fill about one 8X11 inche page on a word processor with a 12 inche font and double spaced. To give yourself a guestimate, google some writing prompts and try to answer them with 250 words but less than 300.