The executor often arranges the deceased person's funeral, although this is not a legal responsibility. There are a number of web sites and books that provide excellent advice on arranging funerals, but here are a few starter tips:
Don't try to do handle all this yourself; enlist other friends or family to help with the arrangements, getting the word out, and so forth. If the decedent was a veteran, there are additional resources available as well.
If you know whether the decedent preferred burial or cremation, it's best to honor those wishes. If you don't know what the decedent wanted, you can check the will, a durable power of attorney for health care document, a separate document sometimes called "final arrangements", or the presence of prepaid arrangements in the decedent's papers.
Burial: Traditional burial is more expensive and involved, but the funeral home or mortuary can guide you through the process. All together, a traditional burial will likely add $5-$8K to the cost of a funeral (including such things as the burial plot, burial marker, a burial vault for the casket, the actual burial, etc.).
Cremation: Almost half of all deaths in the US are handled via cremation, which is substantially less expensive than burial. Cremation typically costs $500-$1500, although electing a fancy container to hold the ashes will increase the price somewhat. Aside from price, another benefit of cremation is that rather than having to rush to hold an immediate burial service, you can hold a memorial service whenever you want, perhaps after things settle down a bit, out-of-town relatives can arrange to return, and so forth.
Military Service: If the decedent was a veteran there are additional options to consider: see Veterans.
A "standard" funeral, including a casket, will probably cost around $6-10K (plus any burial costs, which can be substantial), with the caveat that funeral costs vary significantly by region and by service choices. The National Funeral Director's Association maintains a list of average costs for various funeral elements. The basic services fee is around $2K, but when you add in things such as a casket, transportation, use of the facilities for viewing, and so forth, the price climbs significantly. TheFuneralSite maintains an even more extensive list, but be aware both sites include items that not everyone uses.
Discount $$: EstateExec users can access discounts on funeral (and other) flowers, saving up to a maximum of $300. See Task: Arrange funeral.
Typically, the executor or another relative will pay for the funeral, and be later reimbursed by the estate once the executor has access to estate funds. Alternately, you can try to get the service providers to agree to accept delayed payment directly from the estate. Whoever pays the funeral expenses should be reassured to know that in cases where the estate is insolvent (owes more than it is worth), the law gives paying these expenses a high priority, along with taxes and probate court fees.
Veteran's Benefits: If the decedent was a veteran of the US military, you may be able to get financial assistance with the funeral, burial plot or other benefits. You can find information on the U.S. Department of Veterans Affairs Burial Benefits web page, or you can call Veterans Affairs at 1-800-827-1000 or your local veterans agency. You can also inquire about veteran's survivor benefits.
As part of this process, you may wish to publish an obituary in a local newspaper (typically for a fee). Legacy.com provides a convenient way to find and interact with the appropriate newspapers, or your selected funeral home can do it for you.
See also First Week.