There are some spring-flowering bulbs that do better when planted in the green (when they have flowered, and still have leaves). You will not get flowers the current year, but the years to follow if you use this method. This is used for new plants, and for dividing existing clumps. Other bulbs are either planted in autumn, or in spring once frosts have past.
Snowdrops should always be planted in the green. The RHS says that this should be done when the leaves are dying back, however these is much discussion about this, and other gardeners have found that planting them while still in flower works as well, if not better.
Winter aconite, with their cheerful yellow flowers, and frilly green collar are now said to be better planted in the green as well, though there is discussion about this, and it does seem to depend on which supplier you get them from.
Bluebells, and tete a tete daffodils can be planted in the green as well, though this is usually done pre-flowering to get a later display of flowers. (see how to plant bulbs in autumn)
How to plant / divide bulbs in the green: Carefully dig up the clump, ensuring not to damage the bulbs or foliage. Shake off the soil, and carefully tease apart the individual bulbs, leaving the foliage in place. Dig a suitable hole ( 3 x the depth of the bulb) and plant leaving the foliage sticking above the soil at about the same level it was originally. Let the foliage die down naturally and wait till next spring for your show!