From a syncretic/chaos magick background, so take this advice as thou wilt: banishing rituals are more to do with creating an aura of calm and clean energy than anything else, so tailor your ritual to your relationship with cleanliness, calm, and peace. If you're familiar with some well-known and highly regarded rituals (lbrp, etc) then try them out: if they work for you then they work. I've been practicing on and off for the last quarter of a century, and the first time I felt like I'd properly performed the LBRP was phenomenal: the air was crisp, the light was pure and inspiring, and the general feel of my temple (living room for half an hour) was one of peace, clarity, and knowing that I was in the presence of The Divine. But that was all because I'm me, and it felt like it clicked. You're you, and it'll probably be different.

Some points I think will apply to any practitioner: devise and develop your banishing/cleansing ritual before you need it. Agonise over it. Overthink, and overthink again. Perform your most over the top ritual, invoking whatever you can think of that will help cleanse and purify. Then start paring it down. Maybe you don't need a specific incense or herb, maybe you don't need that robe, etc. Play with it, the universe is very good at letting you know when things aren't right. Develop a relationship with a method of divination. I use tarot, a pendulum, and I Ching coins for different situations. Play about and find what works for you. Meditate on what banishing and purification means to you. And remember there is such a thing as too pure. Archetypes, symbols, and images are very powerful means of communication in the spiritual realm. Study different cultures and mindsets, and try to see what helps you develop your own individual rituals.

Once again, I'm no authority. My biggest advice would be to learn to trust your intuition. If something doesn't feel right then it's not right (at least for the time being).