They have personalised fitness programmes to undertake during the close season. Often they have to report back on a weekly basis so that readings such as pulse and weight etc can be taken.
a couple of weeks off i imagine, probably less. They're professional athletes so i wouldn't be surprised if they don't have much "time off" for excercise.
Most teams will be back by 1st July but some managers will have them back in mid June. What you do in that time is up to you but if you care about fitness you'll keep it up during your break.
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While Kieron Dyer had pretty much his whole career as a vacation.