This is a ritual to invite Brighid into your home to be your hearth guardian, or to renew your acquaintance with her if she is already that. It may also be used to ask Brighid for favors, or simply to enjoy her presence.
If you have an image of Brighid, put a candle or oil lamp in front of it. (An image is not necessary; the flame itself is an image.) If you are fortunate enough to have a fireplace, lay a fire in it instead, but do not light it. In front of your fire source, put a bowl. Next to it put a pitcher of milk. Stand or sit so you are at a comfortable level with respect to the fire. Extend your arms, bent up at the elbow with your palms facing forward. This is called the "orans position," and is a common one for Pagan prayer. Nod your head or bow to the fire source and then say:
I invite you into my home,
you who are the Queen of the Hearth,
you who are the fire's bright flame,
you who are the burning shining.
I call to you, Brighid, to come to me.
I ask you, Brighid, for your bright presence.
Light the fire source, saying:
The fire of Brighid is the flame on my hearth.
Pick up the pitcher in your right hand. Hold it up before the fire (you may put your left hand under it to steady it if necessary), and say:
A gift for you, Brighid of the Cows, A gift for you, Brighid of the Blessings.
Pour the milk into the bowl, saying:
My prayers are poured out with this milk My words and deeds flow straight to Brighid.
Put down the pitcher, and, if you have a request, make it now. (I usually pray to Brighid for healing, inspiration, or home protection). If you are not making a request (and it is good to just commune with the goddess for a while from time to time), sit or stand in meditation on the flame. A good mantra to use is, "The fire of Brighid is the flame in my heart," while visualizing a fire burning in your heart. This mantra may be used at other times, to renew or establish a relationship with Brighid, or just to feel her comforting presence. It may be considered an offering to her in and of itself. When you are done, extinguish the candle or oil lamp, saying:
She ever burns, Lady of Fire, in my heart, in my home, on my family hearth (or "every hearth" if you live alone.)
Take up the orans position again, nod or bow, and the rite is done.
If you are using a fireplace, use the same words and the nod or bow, but leave the fire going. Spend some time by it, especially as a family. Brighid likes that.
Leave the bowl of milk in place for 24 hours, and then put it outside for the land spirits.