If there is dirt under the raised bed, you can add as little as 6 inches of soil on top. A mix of compost (you can purchase it) for nutrition, perlite or vermiculite to keep the soil "fluffy" and peat makes a good mix. this is the Mel's Square Foot Garden formula. My first year I added Kellogg's ammend to regular dirt, but I has better success with Mel's mix. We had a vegetable garden on asphalt at my school and grew broccoli, lettuce, strawberries and a few other vegetables in 6 inches of planting mix.
Six hours minimum sunlight is essential.

Here is a link that might be useful: Raised vegetable garden

Too late? No. Sure the ideal is to get them well established months before use but with some extra work it can still be done.

2. How will it be enclosed? Will you be using the existing soil in addition to additives? Will you be tilling up the existing soil or just using it as a base? If enclosed with sides then you can just lay down a layer of cardboard to prevent weeds and pile amendments on top of it - purchased compost, composted manures, good potting mix (do not use Miracle Grow Garden Soil), peat, etc. OR you can mix all of that in with the existing soil.

3. 6" minimum, 8" is much better (especially for tomatoes), 12" is best.

Check out the post titled "Raised Beds...Working On" for more info and pictures and I linked more photos below.

Dave

Here is a link that might be useful: Raised bed garden pictures

Last year I started in March to build 20- 4' x 4' raised beds on top of existing soil. Each one was 10" to 12" deep.
I fill them with about 4" of my own compost and topped off with top soil purchased locally, $25 a yard. They delivered 7 Yds. I added a little lime for any possible high acid. I also put a layer of cardboard or multiple layers of newspaper.

If you have gophers, don't forget the hardware cloth! Nancy

not to late at all if you use compost and composted manure
I once set up bed on April first and planted out on April 15.
over wintering for settle soil only matters if you using fresh manure.

This is my 2nd year with raised bed. I won't go back to anything else (except containers). No more digging into the ground itself. So much easier and NO weeding. I used cinder blocks for the borders of my bed.

1st came 4 raised beds, then came fences, rails, climbing plants, raised bed for garlic, now this ..a cold frame..
look at the fun your going to have

2. What's a good way to get the soil ready for planting?

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The easiest (and most expensive way) is to buy soil.

The least expensive (but most difficult method) is double-digging. "Double-digging involves removing the topsoil the depth of a spade, setting the soil aside and then loosening the subsoil another spade�s depth. Finally, the topsoil is returned with added amendments, such as compost, manure or fertilizers.

Me, I took a sorta hybrid approach with the understanding I would spend a couple years improving my beds rather than kill myself with all the double-digging. I built my beds & covered the turf with lots n lots of newspaper. I filled them with free horse manure, peat moss, vermiculite, perlite & compost.

The first year wasn't spectacular, but i was gardening with a moderate amount of effort & money. Each year since, I've continued to amend my garden with compost (and look for new spots in my yard to make raised beds).

TN
After doing what I did, you took the best approach IMO