Wild turkeys mate around mid march to late may depending on your climate, however domestic ones start as early as january through september(also depending on where you live). They will lay untill they have a full clutch, but if you take each egg they lay, you'll get around 80-100 each bird depending on her age.
Turkeys do not need a male to start laying, they will drop an egg about every other day. Generally you can hold eggs for about 14 days or so before the viability starts to drop off. An of course you do need a male for them to be fertile. The hens will have there own "nest" or have a community nest. A nest is where ever they decide to lay.
If you have males they will mate about a week to two weeks before they start to lay.