If it is necessary for you to send a letter of sympathy for a grieving family, consider sending commercially sold funeral cards as a convenient option. You can offer the note with a flower bouquet or by itself. If you are remotely located in another country, it is also acceptable to send a message through email.
You may be able to find nice notes at a neighborhood bookshop. It is also a good gesture to write a message yourself. If you are handwriting is not clear, you should remember that there are store bought notes with pre-printed messages that you can just sign and mail.
Offering a sympathy note is something usually expected in most cultures. They can be given whether you attend the memorial service or not. It becomes more of a necessity if you cannot be at the wake. If you are mailing the note, you can give it before or after the actual burial.
In response to your note of sympathy, the family of the deceased is also expected to send thank you notes to those who were at the service and to people who send letters of sympathy. A family member closest to the dead person usually writes and sends them. Expect to receive one in the mail a week or two after the burial.
Sending a bundle of flowers with a note is also common practice. Try to send a bouquet during the wake, before the actual burial. You can have a flower delivery service do this for you. Just make sure that the blossoms come with a personal sympathy note from you.
You can get professionally made note-cards at a bookstore, from a craft store or on the internet. Before making a purchase, read the message inside to make sure it is appropriate. Most people add their own message with store bought funeral cards. You can do this too and make your message more personal and special.