The ancient Greeks made amazing temples and folks from all walks of life would travel (sometimes great distances) to give offerings and worship the Gods of Olympus, but there were also altars and dedicated spaces to specific Deities in more humble places. These were simple altars, very basic, not the grand massive temples that we all have seen pictures of. These 'home temples' were smaller and simple and places where daily personal offerings were given to Patrons and Patronesses. Worship places were also kept out in nature, in liminal spaces (like the gate of the city), and in hidden spaces. The large temples were built keeping the natural landscape in mind, so that the temple added to the natural splendor of nature rather than eclipsing it.
Hecate is believed to have been worshiped mainly in the household; and what this tells us is that She was much more pervasive of a Goddess than some of the other Gods of Greece. Throughout the histories Zeus upheld Her, She was the daughter of the Star Goddess and related to Phoebe, who is the Titaness that is the moon. In fact, Hecate is a Titaness herself and she was the only Titan who aided Zeus in the battle of the Olympians versus the Titans, which would explain why she remained in the stories long after the Titans had been locked away.
There is reference to Hecate being the main focus of honor during a religious ritual called Deipnon. Depinon was performed during the evening meal every New Moon. During this ritual food was offered to Her and to the restless dead. There are three parts to a Hecate Deipnon; first, the meal was offered to Hecate by leaving it at a crossroads or the entry way of the home, second, the Goddess would take her share, and then finally the home would be ritually cleansed and cleaned.
Hecate is often depicted carrying torches, one to shine light down both avenues of the crossroads or perhaps one to shine Her way and one to shine your way down the path. She also carries a key, which shows Her connection to the front door or the gate of the city. She knew about plants and medicine and was considered a sorceress. She is described giving instructions on how to both create healing tonics and poisons several times in the stories; which is why She is connected to plants known for their dangerous natures, like belladonna, dittany, mandrake, and aconite. She was seen as a triple faced Goddess, likely due to the fact that She could see down the different paths and originally Her faces were not human, but seen as a dog, a serpent, and a horse. The connection to dogs is very telling in Her role as guardian of the town. The first creatures that would give warning to intruders would be dogs and this was considered Hecate's warning.
The name Hecate can be translated in many ways: "will", "She that operates from afar", "She that removes", and "the far darter" are just a few of the names She was called.
We have some information on how She would have been worshiped by Her original people, but over time and with the growth of the modern Pagan movement, Her worship has shifted and grown. Her role as Queen of Witches is one of the areas where Her power has grown and developed; and it is largely a modern construct. This "new" connection or correspondence doesn't mean that it is weaker than Her ancient role; in fact, these modern connections are likely stronger than her historical ones. Her modern energetic is a living force, it is in the modern Pagan awareness, it is being worked, and these modern constructs are, in reality, what is keeping Her alive.
In your own work call upon Hecate, and her torchlight, to help guide you to your inner witch. Call upon Her to help you learn herbs and spells. Let Hecate guide you as you walk between the worlds and be in liminal spaces, but just make sure you give Her proper tribute. The ancient Greeks knew that nothing comes for free, the Greeks Gods want payment before they work on your behalf. Our modern worship of Her might have changed, but this is still very much the case.