many will honor their chosen deity by an avatar like a picture or a statue
some chose to honor by use of their element
particular rituals depend on your preference, time of year, god/goddess you honor, etc
My favorite goddess I would have to said Athena Greek goddess of Wisdom and peace. I honor her by keeping my heart pure and thinking of her as a friend. there a lot way I can honor her but this the way I like best.
I follow Athena as well, but don’t identify myself as a wiccan. I prefer to honor her by letting wisdom guide my actions, rather than emotion. I can’t really offer anything or burn incense since I live in a dorm and that is a no-no. 😉
The most important way to Honor ones Deity is to live a good life according to the Wiccan Rede. If you don’t do that nothing else would matter, and as to the nature of the actual ritual that is something each Wiccan decides for themselves, unlike more doctrinaire faiths there is no prescribed set of rituals to which all must adhere. It is also a commonly held Wiccan belief that All Gods are One God and All Goddesses are One Goddess, so the actual name and aspect would be purely a matter of personal preference as well.