Do they have some kind of a magical funeral or are they buried in a usual muggle cemetery?
It seems that there is no specific ritual. Lily and James were buried in a more or less normal graves in Godric's Hollow:
Harry Potter Wikia, where this image comes from, also states that Ignotus Peverell (the original owner/creator of Harry's Cloak of Invisibility), as well as Ariana and Kendra Dumbledore lay in the same cemetery.
Same Wikia also notes that the St. Jerome's graveyard, where the mentioned persons lay, is for both Muggles and Wizards.
Alternatively, wizards can be cremated, along with their wands, as ThruGog points out in their answer.
However, Dumbledore had a special funeral ceremony (image from Pottermore):
and a tomb on Hogwarts grounds, next to the lake: