What is common practice? What does it usually cost? Should I be thinking about this?
My understanding of life insurance is that it usually provides some amount of money when the beneficiary dies. They don't divide the benefits into "funeral costs" and "all the rest". At least, mine doesn't seem to.
Also, a recent Wall Street Journal article on the casket-making industry noted
The average cost of a traditional burial is $7,200, compared with $1,400 for the crematory fee, some form of memorial service and an inexpensive urn, says John Ross, executive director of the Cremation Association of North America. (cite)
It may also be important to check the policy for how long to process the payout and also how funeral homes expect to collect payment. All the life insurance in the world won't help funeral costs if it comes months after passing. I have no experience with this matter, but it's an aspect to consider.
Another consideration is that the beneficiary of the life insurance policy may not be the person responsible for paying for the funeral. I'd expect the funeral expenses to come out of the estate of the deceased (if there are any assets there). The other answers regarding the likely timing of the expense vs the life insurance payout are very good as well. As @SpecKK said, an emergency fund is probably the best way to go.