I will start by saying that Disneyphile can answer this better than I - she is far more edumucated in the Wiccan ways. I will (with the help of GusGus) give some basics.
Since you aren't experienced with full rituals, we will avoid heavy details.
Some basic thoughts:
- Banishments work best during a waning moon (the time between a Full Moon and a New Moon). Unfortunately, today (7/1) is the last day of waning moon. The next full moon is July 18, so any time after that would work. Again, a waning moon is not a must; it just helps.
- Remember that you are only banishing the MEMORIES of this person and the relationship: you do not want to wish harm upon the person as part of your ritual. The rule of three is strong within Wicca: everything you put out into the Universe will come back to you three-fold (known as the Three-Fold Reed).
- If you have an item(s) to burn as part of the ritual (physical items that are reminders of the person you are trying to banish from your life), make sure they are non-toxic. You don't want to be polluting when you are banishing (Harm Ye None, Lest Ye Be Harmed).
- Only burn stuff outdoors.
- As far as what "ritual," it looks like ABG covered the basics while I was writing. That should cover you pretty good.
- But I do (slightly) disagree with ABG on one minor point: Sage is more for cleansing and purifying. It would be great for cleansing your body after the banishment. Bay Leaf is good for Protection, Purification, and Healing (and is easy to find as opposed to some other herbs such as myrrh).
- Also consider burning some sweetgrass after the ritual to seal in the cleansed goodness.
ETA:
This site covers far more of the process than you probably want to know on Banishment rituals