Beech
The great favourite of so many turners! It dries quickly and with little degradation Is best felled in the winter months and being very susceptible to insect attack should be cut up into billets, bark stripped off and stacked as above without delay. Covering up end grain is not essential. Commercially supplied beech, somewhat redder in colour, is often presteamed to kill off fungi spores. That may tell you where that nice piece of spalted timber came from!
Birch
garden birch is likely to be small stuff but still quite useful for turning. Fell in spring if possible, remove the
bark and saw into billets. Stack as before with weights at the top to prevent warping. Being prone to fungal infection quick drying (to which birch responds well) is advisable. By starting the process in early summer with largish separators- 30mm is ideal– considerable drying will have taken place. When the colder, damper weather arrives its best to transfer the timber to a sheltered spot like a shed which had less moisture than out of doors.
Boxwood
Quite scarce so its valuable and needs to be tackled carefully.
Convert to square edged stock shortly after felling, which is best done in winter. Even then it dries very slowly and is liable to develop fine surface cracks. This should be kept in mind when deciding the size of timber required.
If dried in the round expect very severe splitting. You might minimise this by adopting an old trick from the past :saw into the log at both ends making deep cuts. Although other methods have been suggested at various times, air drying ,in a careful and straightforward way, is perhaps the best way for most of us .
Try to speed things up and you most likely will cause more splitting or worse.
Interestingly seasoned box may only just float . Does that help?