1 Do you worship The Goddess?
We don't worship a monolithic Goddess that is made up of all other goddesses. We worship individual goddesses, who each have their own unique personality, as well as gods. (Except for certain people who only worship goddesses- or however you want to phrase it)
2 Which gods do you worship?
Deities that were worshipped in ancient Celtic cultures.
3 So you worship all the Celtic Deities?
Not necessarily. Most Celtic Reconstructionists focus on a particular culture, such as Welsh (deities include Don, Lleu, Arianrhod, Gwydion) Gaulish (Taranis, Epona, Cernunnos, Rosmerta)
or Irish/Scottish (Danu, Dagda, Morrigan, Brigid, Lugh).
Besides, there are also some Celtic deities that we know very little about, or ones that were worshipped in the past, but that we have no record of.
4 So should I just pick a Matron or Patron from a list of Deities and swear oaths to Them?
You don't choose a patron deity, they choose you. Not everyone has a patron, and that's O.K. Also you don't need to swear an oath to a deity or anyone else to belong to this tradition. (Heh heh, I'd like to quote the person on this community who said "you don't have to take Lugh as your personal savior or anything")
5 I want to do a ritual, which Deity should I use?
Firstoff, you don't "use" a deity, you honor one. Some holidays and rites of passage may have particular deities associated with them- Imbolc is Brigid's festival, Taillte & Lugh at Lughnasagh for example. Research the customs and traditions surrounding the ritual.