A very dear friend of mine is a Jew, certainly not Orthodox but I
suspect that he might like a Jewish funeral and, if he falls off his
perch before me, I would expect to be invited.

I understand that Jewish funerals are very hasty affairs ... How they
do it is beyond me but, for no particular reason, I thought, 'Should I
wear a hat in the synagogue?'

I am not expecting anything to happen within the next 100 years but
... you never know.

Could someone please tell me what the form is?

I am a non-believer who lives in the UK (if that matters).

Hello and thank you for your question.  This is my first opportunity
to answer one of your interesting inquiries.

As to whether you should wear a hat in the synagogue, I would suggest
that you wear a yarmulke (also called a kippah) indoors instead.  No
need to obtain one in advance--they will surely be available at the
door.  While it wouldn't be wrong to wear a conventional hat, the
ceremonial head-covering would be more in order.  And it would be
wrong to be bare-headed if the congregation maintains the practice
(there may be some Reform groups that worship bareheaded--in that
unlikely event you could be bareheaded as well).

"Over the last 300 years, traditional Jews have been well known for
wearing hats or some other type of head covering. In some European
communities, the hat was transformed into the smaller yarmulke
(Yiddish)/ kippah (Hebrew). Yarmulke might be an acronym for the
Hebrew expression, "Yirey m'Elohim (Be in Fear of G-d)." That means it
was worn in respect or reverence for [God]. Kippah is the Hebrew name
for the head covering and it means "covering". Whatever forms the head
covering may take, the lesson is clear."
Why Do Men Wear Head Coverings?
http://216.239.41.104/search?q=cache:5TJFqpXjY5gJ:www.kehilatdvarhashem.org/kippah.htm+yarmulke+hat+attire&hl=en&ie=UTF-8
[Google Cache]

In researching this question, I came across lots of other advice about
Jewish funeral behaviour.  But some of the advice seems excessive and
even silly--for example that one would say "May the Eternal One
comfort you amongst other mourners of Zion and Jerusalem" to the
bereaved.
http://216.239.41.104/search?q=cache:BfrrDcAPzwYJ:www.nvo.com/finalplans/nss-folder/htmlcode/funeralcustomsandetiquette.html+jewish+funeral+courtesy+hat&hl=en&ie=UTF-8
[another Google cache]

A correct bit of advice, however, is that one does not send or bring
flowers to a Jewish funeral.
http://www.ruthie.org.uk/customs.html
What Should I Send to a Jewish Funeral? 
http://www.beliefnet.com/story/19/story_1930_1.html

Gifts are not required or expected at a funeral.  It would be kind to
make a gift in your friend's name to an appropriate charity (not
necessarily a religious organization, but one that reflects what you
know of his interests), and your friend's family would receive notice
of the gift by post.

As for the hastiness--the rule is simply that one should be buried
within 24 hours of death if possible.  There is mourning period for a
week following the funeral.  It's called shiva, a 7-day period when
the family remains at home to visitors (gifts of food are appropriate
at that time).
Jewish Funeral and Mourning Customs
http://www.jdcc.org/sepoct97/doc1.htm
Saying Goodbye to a Loved One: Jewish Funeral Customs
http://www.ujc.org/content_display.html?ArticleID=1598

A somewhat pragmatic funeral director tells us that 72 hours are now
acceptable between death and burial, with the extra time being excused
as travel time.
http://www.sagelfuneraldirection.com/faq.html

By the way, there is normally a meal for the mourners and guests
immediately after the burial.  You'll wash your hands before eating,
and possibly there will be a pitcher of water for people to pour onto
their hands as a sort of public washing.  It's generally a somewhat
upbeat affair--more like a Wake--while the shiva visit will tend to be
more solemn.

And at the gravesite, if you see people lining up to sprinkle dirt on
the coffin after it's been lowered into the grave, it's OK to join in.

Finally, there is a ceremony called the 'unveiling' when the headstone
is officially dedicated, traditionally a year after the funeral.
http://www.weilfuneralhome.com/mourners6.html
  [I regret to say that when as a child I was told we'd be attending a
relative's unveiling, and I thought the deceased was going to be
revealed after a year in the earth.]
And if you visit the grave at or subsequent to the unveiling, it's
good form to take a pebble from the earth and leave it on the
headstone.

Search terms used:
yarmulke kippah
jewish funeral 24 hours
jewish funeral etiquette

I hope this sets your mind at ease, and that you and your friend both
live a long time!  Thanks again for bringing us your question, and do
feel free to request clarification if needed.


Sincerely,
Richard-ga

Great, Richard, Many thanks.

I now feel prepared, should I ever be required.

You've thrown in lots of interesting extras, too.

Warmest regards

Bryan

Overall, Richard-ga got it right. And his links provide more info as well.

However, there are two mistakes in the info that Richard-ga found.

1) The folk etymology for "yarmulke" -- which is cute, but not at all
serious -- is that it's derived from "Yeray Malka," Aramaic for
"fearing the King." The suggestion ""Yirey m'Elohim" would make no
sense in Hebrew or Aramaic. Furthermore, that suggestion is from a
website of Hebrew Christians, who are not exactly known for their
accuracy in presenting Judaism.

2) The statement to mourners that begins ""May the Eternal One..." is
not recited at a funeral, only at the shiva (which starts after the
burial). Furthermore, when describing other people's religious
traditions, to slander one as "excessive and even silly" is simply
disrespectful. I expect more from Google Researchers.

-- Ravuri-ga

Hi, Ravuri

Many thanks for your Comment which is much appreciated.

I am quite sure that, in no way, did Richard mean to be disrespectful.
Certainly, it did not seem that way to me and, really, I was only
looking for some general guidelines for the eventuality that my dear
friend might pass away before me.

However, I find that Comments (such as yours) contribute to a wider
understanding, and this is great!

Many thanks

Bryan

I'm Jewish and have a few comments on this answer.  I hope my personal
experience proves helpful.

Clarifications:

"While it wouldn't be wrong to wear a conventional hat, the ceremonial
head-covering would be more in order."

In my experience, unless the service is at a reformed synagogue which
tend to be less formal, it is inappropriate to wear a conventional
hat.



"Yarmulke might be an acronym for the
Hebrew expression, "Yirey m'Elohim (Be in Fear of G-d).

Yireh m'Elohim doesn't mean "Be in fear of G-d" in Hebrew (I speak
Hebrew fluently).

Yireh  translates as "[he] will see"
m'Elohim as "from G-d"

So translated literally from Hebrew, it means "He will see from G-d." 
Who knows, maybe it's profound.


"As for the hastiness--the rule is simply that one should be buried
within 24 hours of death if possible. "

The rule is within two days of death.  I don't know where the
researcher read "24 hours" but it's two days.  The link provided
confirms this:

"The mourning period begins with the funeral. It is tradition for the
burial to take place as soon as possible, even on the same day of the
death, but no more than two nights after the death."



"A somewhat pragmatic funeral director tells us that 72 hours are now
acceptable between death and burial, with the extra time being excused
as travel time."

Be careful in confusing the opinions of funeral directors with Jewish
law.  Jewish law is not fluid and changing.  Any straying from this
law is a branch away Jewish customs, and a more modern approach at the
expense of tradition.



"And at the gravesite, if you see people lining up to sprinkle dirt on
the coffin after it's been lowered into the grave, it's OK to join in."

In my experience, usually each person will shovel one heap of dirt on
the grave, beginning with the immediate family, and including anyone
and everyone who wants to participate.


My advice: 
In general, though, the focus at a friend's funeral won't be you. 
Just be respectful, and participate in customs as they arise and you
feel comfortable.

Many thanks, Res3

Of course, I'm hoping the situation won't arise for many years but I
now feel better prepared for the eventuality should it arise.

Warmest regards

Bryan