Disposing of the bones or ashes (asti) in the Ganga:
One should bathe in the Ganga, and performing achamana, facing north, holding sesame and water one should perform the sankalpa as follows;

 visnur om tat sat
 adya ...............................masi (........name of the month)
 ........................................pakse (light or dark fortnights)
 ........................................tithau (phase of the moon)
(name of departed) ..............................................................dasasya etany asthini gangayam viniksipami
(On this tithi, of this frotnight, of this month I dispose/throw the bones of ................in the Ganga.)

The person should chant the purification mantras over panchagavya, one moves his brahmin thread (yajnopavita), placing his yajnopavita over his right shoulder instead of the normal left, then one should wash the bones with the panca gavya.  Mixing the bones with gold, honey, ghee and sesame, he should seal them in earth, and holding the earth in his right hand he should say:

   om namo'stu dharmaya
    (I pay my respects to dharma.)

Entering into the water he should throw the earth into the water saying:

   om sa me prito bhavatu
    (May he be pleased with me.)

He should submerge himself in water, then come out, look at the sun, and give gifts in charity.

visnur om tat sat
adya .....................masi
..............................pakse (dark or light)
..............................tithau (phase of moon)
..............................gotrasya (name of gotra or line ISKCON is Acyuta gotrasya)
(name of departed)...........................dasasya krtaitad gangadhikaranakasthi niksepa karmanah samgatartham daksinam idam kancana mulyam
sri visnu devatam yatha sambhava gotra namne brahmanaya aham dadami

Dahana Adhikari (Claimant to the last rites):

There is a specific order of precedence of the person who should perform the last rites including burning of the body.
The order for a deceased male is as follows:

The son, from eldest to youngest, their sons, sons of their sons.
The wife, either childess or with children.
Unmarried daughter, betrothed daughter, married daughter.
Daughter's son.
Youngest to eldest brother.
Youngest to eldest half-brother.
Youngest brother's son, oldest brother's son.
Youngest half-brothers son to oldest half-broher's son.
Father, mother.
Daughter-in-law
Step mother
Grand daughter, married grand daughter (through the son)
Wife of great grand son
Great grand daughter
Father's father, Father's mother etc. ,
other relatives including uncles, cousins,
Disciple, guru, priest, friend, friend of the father ,
Resident of the same village of same caste,
King.

Order for a deceased female is as follows:
Eldest son, to youngest son
Sons's son
Great grand son through male lineage
Unmarried daughter, bethrothed daughter, married daughter
Daughter's son
Husband
Daugher-in-law etc.
Disciple or student of husband or self .

A brahmacari should avoid performing funeral rites, but if others are unavailable he may perform rites for parents, grand parents and guru. The parents of a brahmacari should perform his funeral rites.

The example of Sripad Madhwacarya doing the last rites for his parents, even he was a sannyasi, because there were no other family members who could do. He did so then resumed his functional service as a Vaishnava sannyasi. He was criticised by some for doing this, but he did it none-the-less.