I have done this ritual with people from many different religions. As long as the people are comfortable with the idea of being around spirits, or of honoring the dead, they usually don't have any trouble. There's nothing here that forces someone to pray to a foreign deity, or eat anything sacrificed to deities or spirits.
When invitations are sent, I always ask people to bring a potluck dish, musical instruments if they play, and that they may also bring divination tools. While children are welcome, I make sure that parents are aware that the ritual will probably be boring for very young children and that they are not likely to have much fun with it unless they're able to keep reasonably quiet for a while and are okay with being still during the ritual.
You'll need at least two people to help with the ritual, for the Samhain Dance invocation of the ancestors. These people should be able to carry a rhythm and chant against each other without stumbling as they each chant something different. If you have more people, it will be a bigger sound, and you can also include percussion weaving in with the chants and poem.
The space should be cleaned and set up for a potluck or feast for as many as will be attending the rite. If you're doing this ritual for a large number of people, it is often best to provide at least one main dish to serve everyone (I usually provide a turkey, a salmon, and something vegan to cover all my different friends' needs) and some drinks, and ask those attending to bring side dishes, drinks, and desserts.
Prepare an altar space with a table or flat area for candles, offerings, and images of deity or other images. Fall leaves, apples, pine cones, autumnal flowers, and other things that remind of autumn, winter, death or darkness are appropriate. If you have an image of Manannan of some sort, this is very appropriate. The altar should have wall space behind it for hanging pictures, or shelves set up for putting up pictures, written names, or holding mementos of the dead.
The altar should be pre-set with a basket or bowl of apples or other fruit and/or nuts as a preliminary offering in the ritual.
Ask people to bring photos or mementos of some sort of their beloved dead. Some will bring things associated with people, others with animals, and this is fine. If we believe that animals have souls or spirits, it makes perfect sense that people would want to remember them too.
You'll need candles (tealights in their cups are great), incense of some sort if you like, plates and cups for offerings of food and drink, nice paper for folks to write names or prayers on if they haven't brought or got photos or mementos, pens for writing, perhaps a cauldron or other fireproof container for burning the papers afterwards.
You'll need a small container of honey, and one of salt.
Proceeding with the ritual:
Welcome the people into the space in any way you wish. It's traditional in the Highlands of Scotland to welcome people with a sip from a quaich (cuaich or cup, but in this case a shallow one with two handles, usually used to ritually serve a sip of scotch to everyone). The quiach doesn't have to contain alcohol. Any liquid will do. Welcome with appropriate words to the season, and tell your guests why they've come to the occasion.
The ritual is for feasting and welcoming the spirits of the dead. It is a profound occasion, but not one that must be solemn. The feast is not a dumb feast. It will not be held in silence, but if people wish to keep silence, they may.
When the guests have been welcomed, have them put their photos and mementos on the altar. If they haven't brought any, offer them the paper and pens to write names or prayers to put on the altar instead.
Smudge the area and people with juniper smoke or have some juniper oil in a diffuser. Juniper was traditionally used in Scotland to purify the house at the new year. This is just a smaller-scale treatment of the idea.
When this has been done, pass around the small container of honey. Each person should take a bit of honey and put it on their tongue (or mimic the action if they have trouble with sugar).
The honey represents the sweetness of life. You can speak of this as the honey is passed from hand to hand. You can be as short or long about it as you like, but short and sweet is best.
Pass around the container of salt. Each person should likewise take a bit of salt and put it on their tongue.
The salt represents the bitterness of death and parting. Again, you can speak of this as you've spoken of the honey.
When this is done and all have partaken, at least in gesture, pray to Manannan mac Lír. He acts as the psychopomp or guide of souls to the land of the dead.
Prayer to Manannan in Irish/English:
Manannan, a Thírna nan cheó
éist le ár ghuí agus osclaím nan n-geatai bíseanna
Manannan, a Loingseoir Mhór
Más é do thoil é, spré do clóca-cheó
agus beir tú ár shinsear, bier tú na mairbh.
Manannan, Lord of Mist,
Hear our prayer and open the Spiraled Gate.
Manannan, Great Navigator,
If it please you, spread your mist-cloak
and bring forth our ancestors, bring forth the dead.
Here is the poetic invocation. It is meant to be rhythmic and mesh with the two chants. Experimentation will show how the rhythms and chants go together. The chants should be brought in with the invoker starting first one chant, which is picked up by the first chanter, then the other, which is picked up by the second chanter. When the chants are moving strongly with both chanters, the invoker begins the poetic invocation proper.
Now is the eve of winter,
Bones of the dead will rise
from Tir fo Thuinn
voice of the swan
Dance from sunset
into the dawn
And the Gods
in the mist
will call them here
Voice of the dead
will answer our fears
as we dance
in the mist
Death to death
and life to life
Form to form
on the edge of the night
as we move
through the mist
Womb to tomb
and birth to birth
Warmth of the flames
upon the hearth
We are held
in the arms
of the earth
they hear our call
Dance their bones
down echoing halls
like the tide
of the mist
The back chants and/or percussion may go on as long as you like, if you want people to dance for this part. If you don't, then fade the chants out after the invocation in the same way you faded them in -- the invoker joins the "bones of the ancestors, dust of the dead" chant and fades it out, then the "dance the bones" chant and the other chanter fades out, until only the invoker is left speaking the line. It fades to silence.
Introduction to the altar:
At this point the invoker, and perhaps the chanters or other altar attendants, will introduce each individual to the altar. Whether or not the invoker will need assistance will depend on the number of people attending and the way the space is arranged.
Each person in attendance is taken by the hand and introduced to the altar. They are told:
This is the altar for your ancestors, and your beloved dead.
Place their hands on the basket/bowl of fruit.
These are offerings for your beloved dead. Call upon them this night, and celebrate with them. Light a candle for them, and call them home.
At this point, the person's hand is released and they light a candle on the altar. If they're so inclined, they may call upon their dead aloud, they might say the names of their dead, or they may wish to contemplate silently. Sometimes I provide Chinese "Hell Money" for them to offer the spirits if they like. When they are finished, they may go to their seat at the table.
When the invoker and/or altar attendants release the hand of each person, they go back and get the next person, until each person has been introduced to the altar. It's good to have a large altar space if you'll have a crowd, so that many people can be at the altar at once.
Once everyone is seated, the feast is brought out and set upon the serving tables. Before anyone is served, plates are made up with a sample of each of the kinds of food in the meal. The same is done with the various drinks brought for the feast. If there is a lot of food, you may wish to offer different plates for meat, for veggies, for breads, for desserts, etc. The plates are carried up to the altars and offered to the ancestors and the beloved dead. They are asked to participate in the feast.
Once this is done, everyone else may begin serving and eating food. If all goes well, there will be conversation, perhaps music, and if people are interested, divinations can be done at this time.
Thanks to Manannan and the spirits:
These thanks can be done extemporaneously, or you can write a prayer like the one at the beginning of the rite. It's not a "dismissal," it is literally a thanking of the spirits for their presence and of Manannan for opening the mists to bring them to this place. No formal invocation of Manannan was done, only a prayer was offered. As the spirits are traditionally abroad at Samhain, to "dismiss" them from a place to which they have chosen to come is rude. Once they are thanked, they can certainly be asked not to haunt the attendants, but they shouldn't be ritually banished in any way. They will go of their own accord when the season moves to the appropriate time.
At this time, candles should be extinguished if the space will be emptied, or left to burn if someone will be there to attend the space until the tealights burn out. People can take home the candles they've lit for their dead. They can either take home the papers they've written on, or they can be burned to send the memories and prayers to the dead.
Once this is done, the food and drink offerings can be taken outside to an appropriate place and left for the spirits. In the Scottish tradition, once the food has been taken by spirits, the toradh or life essence of it is gone, and it becomes unfit for human consumption. The word literally means "fruit, produce, yield" but is also used in this poetic sense.