You have good suggestions made, especially from Alcove. My 2 cents:
Do yourself a favor and buy/rent a Sanken CS-3 (
http://www.trewaudio.com/products/sanken/cs3/); it's highly directional and just kills noise from the sides and rear. Keep it pointed at the talent up to twenty or more feet depending on overall ambient noise. IMPORTANT - Use a windsock (basket) and keep the back of the mic towards the surf, so your boom operator is sometimes walking in the wet part of the sand; be careful to keep his/her tracks out of the frame, at least long enough that they disappear. If you have to shoot with the mic parallel to the surf, you can further abate the surf noise by using plastic wrap taped around the back and sides of the basket, leaving the front without plastic wrap but keep the front of the basket on.
You got excellent tips on lavs and planted mics, so I won't get into them except to say, try to rent the Sanken COS-11. They are very small, unobtrusive, and have great sound.
To deal with wind, as much as possible, basic to handling a boom mic is keeping the back end of the mic pointed into the wind. At the beach, the wind is gusty so the direction can change. The surf is constant, so reduce it's effect first and let the basket primarily deal with the wind.
And finally, find a experienced boom op to handle the mic; half my work comes from productions that are half shot and still getting bad sound because they are trying to use a PA to handle a boom, or using a inexperienced student in a position requiring skill. And, as suggested earlier, record ambient sound that can be used for clean-up in post. This is the one thing that most indie productions do not do and wind up paying for it later.
Best of luck with it. Let us know how it turns out.