The Samayācāra tradition comes to us from the Divya Parampara, through Bālā Tripurasundarī, who is our Guru. Samayācāra means an internal mode of worship and worship with the fire ritual. We do the homas, we do the internal visualizations. Whether the external pūjā articles are present or not we can visualize them and do the entire pūjā.

The Dakṣiṇācāra tradition comes to us from 
 Siddha Parampara, through Sarasvatī Order. Here you worship the Śrī Cakra. It is a bahia pūjā. You are worshipping something outside of you, usually a vigraham (an idol or yantra). The Suvāsinī pūjā is also done. Suvāsinī is a woman who represents the Śakti, but the pūjā is done only to her feet.

The Kaulācāra tradition comes to us from Siddha Parampara, through the Dattātreya Saṃpradāya. In this tradition the idol is replaced by a living woman, or a man, or a couple. You can also think of Her as the union of Śiva and Śakti. Dattātreya is the combination of Brahmā, Viṣṇu and Rudra. His instructions were codified in Kalpa Sūtra by his disciple Paraśurāma.