The ritual was done in front of my personal altar, which was consecrated a long time ago to the Kindreds.  If I had no specific altar, I would have consecrated the space by either carrying burning incense around it (traditionally, sunwise), or by sprinkling with water, and saying something like:

I consecrate this space,
     In the name of the Mother who bears me,
     In the name of the Father who begets me,
     By the power of the Great Mystery at the heart of all,
And for the purpose of Sacred worship.
So be it.

After the ritual, I would return the space to what it previously was by saying:

May all be as it was before, and yet may I always remember the Sacred place within.

It's not the particular words that are important, but the intent  to set aside, even if temporarily, the special place to worship in - sort of like setting a guest place at your table at home.

This is what I used for the ritual:

A candle in a votive glass, set into a crystal bowl full of water - this has to do with Brighid being associated with both fire and water.  A floating candle would work just as well, or even a taper set into a bowl of water - or however you wish to combine the two symbols.  The thought in setting this up is fairly important, because it becomes the main focus of the Ritual - the Brighid Candle.

incense
matches
offering - I used flower seeds in a small bowl
a small bell
a chalice

I turned on quiet Celtic music in the living room, then went into my office, closed the door, closed my eyes, and meditated for a few moments, relaxing and transitioning.   Then I put on my special ritual necklace, which I always wear for rituals.

Consecration of time:  I rang a bell.

Consecration of self:  I dipped a finger into the bowl of water, saying:

By the birth waters of the Mother, I am cleansed and purified.

I spent a few moments in meditation, focusing on the words I wanted to say, and the sense of blessed quiet and peace.

I lit the Brighid Candle, saying: 

I light the Sacred Fire,
    As Beloved Brighid would kindle,
    As Foster Mother would kindle,
    As Lady of the Hearth would kindle,
In love, and in peace.

I light the Sacred Fire,
    As the beacon unto the Holy,
    As the ward against the unholy,
    As the flame of holiness within my heart.
In kinship and affection.

Great Brighid, bless this Rite.
    So be it.

I took a stick of incense, and bowed low from the waste in the Russian manner (this is traditionally a gesture of great respect, not necessarily submission, though), thrice, saying

<bow>  I bow before my Ancestors, may They be blessed.
<bow>  I bow before the Nature Spirits, may They be blessed.
<bow>  I bow before the Shining Ones, may They be blessed.

I lit the incense, saying:

Beloved Kindreds, great and small,
Hear the words of this, Thy child and Thy sister,
Bless me even as I bless Thee, I pray Thee,
Accept from me this offering of incense as a token of our Kinship.

( I have sang the following lines on occasion when I use incense as  offering in the evening - taken from the Psalms):

May my prayers arise in Thy sight as incense,
And may the lifting up of my hands be an evening sacrifice.

I raised the bowl with flower seeds up in the direction of the Brighid Candle, saying:

Beloved Brighid, Spirit Mother of our Clan,
Hear the words of this, Thy child and Thy sister.
    Fiery Arrow,
    Lady of Wisdom,
    Healer of ills,
Bless me with Thy presence and Thy guidance, oh Shining One,
And accept this offering as a token of my love and reverence for Thee.

This was basically a general kinship ritual, with no specific goal in mind other then general guidance and assistance.  Therefore this part consisted of a prayer and a meditation.

Oh Brighid, and all ye Kindred Spirits,
I ask that Thou bless my Clan and I
    With inspiration,
    With guidance,
    With protection.
Now and henceforth, and forever more.

We are Thy Clan, oh Brighid,
Thy spirit-children, Thy folk.
    That we might not stumble,
    That we might not be lost,
    That we might not fail,
Bless us, or Great One.

For we would serve the Holy in Thy name
And walk in harmony with the Great Mystery.
    So be it.

I then meditated in silence for a time.

I took the glass with the libation and held it up, saying:

Shining Brighid, and all ye Kindred Spirits, share this drink with me,
That we might commune together and be blessed, as Kin ought.

I kept the glass up for a few moments, meditating on sharing with the Kindreds.  I then took a sip, and put the glass down.  <this is later given to the Earth>.   I then stood silently again for a short time, enjoying the sense of kinship - I think I hummed a song as well.

I bowed once again before the altar, saying:

Shining Brighid, Great Kindreds,
I thank Thee for Thy presence and Thy blessings - now and always.
As I prepare to go forth from this Rite,
Know Thee that Thou are welcome at my fire.

I stood quietly for a time, transitioning mentally from the ritual state of mind to the more mundane state of mind.  Then I said

As I have been blessed, so may I carry forth the blessings.
As I have walked with Kindreds, so may I walk with the Folk,
As I have Seen within, so may I see without.
    So be it.

I blew out the candle, saying:

The Sacred Fire is out, yet forever does it burn in my heart.