Be certain that the entity you've discovered is truly deserving of a banishing. Bad intentions can be enough, but trying to convince it to leave of its own accord is always a better option.
Research strong, protective deities that you feel a connection with, and get to know them. Choose one to call on, or maybe two if they're compatible.
Choose herbs that are protective and/or cleansing. Sage, thyme, garlic, black pepper, salt, and apples are recommended. Research the meaning behind any herbs you choose so that you can pour the right motivation and energy into the herbs.
Plan your verbal assault. Choose words that feel strong to you, and that are easy for you to say in a potentially stressful situation. Call upon your chosen deity (or deities) and be sure to demand your wishes. Throw your intention into your speech. For example, "Begone, and never mess with me again in the name of (deity/ies name/s)."
Wait for the demon to be present. Point or cast your chosen herb(s) at it and recite your speech with strength and certainty. Do not back off.
Smudging is the art of purifying an area of evil spirits by burning certain herbs. Sage smells beautiful and is often used in native American traditions.
Feel free to use aspects of your religion to strengthen your exorcism, such as pentacles and chants.
If you feel it's appropriate, learn shielding techniques and other defensive energy work.
One method that has been extremely successful in the past years in the Omni, is the Crystal Binding methods, which was discussed in previous articles, and works in the same way, except you trap the being in the crystal and bury it far away from you. We've used several types of quarts and obsidian, both having great results with it.
Remember, the more powerful the entity, the more energy you must use to send it away. If you feel you do not have adequate power to send it off, you can choose to work in a group or invoke more powerful beings. Sometimes gate work and bindings are needed to be sure it stays away.