I will start off this question by saying, I personally use Deities in my practice. I find them to be inspirational as well as informative. Personally my homage depends upon the Deity which I am honoring. For example: Athena, I may offer her Rose petals using red and white candles, Frankincense and Dragon's Blood. Which leads to my question. For those that use Deities, I am curious to know how you offer homage? If at all possible, please be specific.
Well my Patron God is "Ganapati" so I use Indian way to pay homage. I have an oil lantern that we call "jyoti" that we put infront of the figure and should turn on 24/7. A sandalwood josstick, roses, jasmines and sweets (sometimes fruits or cakes) as well as a beverage (milk, juice or just plain water). I do the "pooja" or worship once a week, usually on Thursday. In worship we chant some mantras and offer the offering as well as ask the deities to stay in our altar to give blessings. In this weekly "pooja" usually we do "Aarti" or fire offering with rice and camphor. Once a year there is a celebration called "Ganapati Cathurti", On celebration I usually bath the figure and clean the altar then perform a bonfire ceremony that called "Homa" to pay homage. we use logs and josstick to burn and we offer 5 kinds of grains (rice,corn,soybean,mungbean and peanut) mixed with butter.