Someone passing from our lives be it human or animal is often a shock. It is perfectly natural to grieve and to question what happens after death. My personal beliefs are that anything with spirit has a choice at the point of death, whether to go to the Summerlands and rest or to reincarnate immediately. Of course eventually once they have learned all they are meant to learn they can spend the rest of eternity in the Summerlands. I also feel that souls of loved ones do watch over us even if they reincarnate. There is always the Dreamworld after all.
I also believe that it is better to celebrate someone's life once they pass than to grieve it. Not to say that we shouldn't grieve. Throw a party for your loved ones when they pass from this life. Death like birth is all a part of the cycle and if we celebrate one we should celebrate the other. Bring together the things that they loved and remember the part that they played in your life. Feel free to express your feeling of sadness and loss, but try to focus on the impact they made with their lives, not with their death. There can be no one set ritual for such a ceremony since all people are different. The ritual should be tailored to the one who passed and those who will be attending. As such it could be a full formal ritual or a simple ritual with no more than a quick invitation to the powers that be to attend.
Here is a basic sample of what I am describing above:
Gather together items that meant something to your loved one. You might also wish to include pictures of them or gifts that they gave you or things they made with their own hands. If they were a good cook or a food lover, feel free to make one of their favorite dishes to share as part of the ritual. Invite the elements, spirit guides and deities that you wish to be present. To open the ritual you may something like, "We have come together to celebrate the passing over into a new life of _______. He/She has touched each of our lives in so many ways. Now is a time to celebrate their life and understand our sadness. Know that _________ is not lost to us, but rather will be a part of our lives in a different way now. Know that they are at peace and the spirits are watching over them." You could then make a list of things that your loved one cared about, asking the guests to add to it. Then open up the floor for people to share, if they feel moved to, how the one who passed touched their lives or brought light into the world. Let people share for as long as they need to. This ritual is really much more for the living than for the departed. You could choose to end it with words along these lines, "_______ Is still with us. She/He was here with us this evening (morning, whatever). He/she will remain with us in spirit." You might want to follow that with future instances where the loved one will be present in spirit, like weddings, graduations, watching young ones grow, etc... For example, "He will be there for Tina's wedding, to walk her up the aisle in spirit form and will be there to watch her children, his grandchildren, grow." Then use any closing that you are comfortable with.
I am personally working to gather together memorabilia of those I love who have passed on to incorporate into an "ancestors" shrine for Samhain. This will include pictures of relatives, pets and other loved ones that have passed. Since the veil between the worlds is the thinnest at Samhain it is an opportune time to remember those that have passed from our lives. I plan to either make a collage or set up the pictures on a common use table (perhaps the coffee table) and then cover them with clear plastic so that they will be present with me visually as I go about my life. I plan to bring out the pictures every year a couple of weeks before Samhain and then put them away a couple of days after. I might work up a personal ritual as well, but I haven't gotten that far yet. I feel this might be a good way to help young children learn to know those who have passed on before they got a chance to know them.
Earth brings us into life
and nourishes us.
Earth takes us back again
Birht and death are present in every moment
Thich Nhat Hanh, Earth Prayers pg 367
Do not stand at my grave and weep
I am not there. I do not sleep.
I am a thousand winds that blow.
I am the diamond glint on snow.
I am the sunlight on ripened grain.
I am the gentle autumn rain.
When you wake in the morning hush
I am the swift uplifting rush
of quiet birds in circling flight.
I am the soft starlight at night.
Do not stand at my grave and weep.
I am not there. I do not sleep.
Joyce Fossen, Earth Prayers pg 30