They vary in different cultures as far as I know.
In my region, we wash the body first, wrap it all in a white garment except the face part. The orifices are blocked by cotton and hairs are covered as well.
Afterwards the body is laid on a makeshift funeral stretcher kinda thing and four people ( have to be younger in age than the deceased with their heads tonsured) are tasked with carrying it to the shamshan (cemetery). While carrying the body a group of people follow it with the procession lead by a priest with a small pot in his hand who chants "Ram nam Satya hai" which is repeated by the members following.
After reaching the shamshan ghat, the body is made to be laid upon a pyre made up of chopped woods and a large amount of ghee is smeared over it to help it burn properly.
After some more Vedic chants and rituals, the priest asks one of the four guys to lit the pyre.
People might wait for a while there, offering their condolences to the next kin of diseased and afterwards head to the house of the head and later on departs for their respective homes. While at their homes, those who were part of the procession immediately take a bath and until they have done so, are not allowed to touch anything.
Also no food is prepared in that particular night in the house of the deceased and they are provided with provisions by the neighbors and other well wishers.
Next day we go to the cemetery to collect the remaining bones and teeth of the after making sure that the whole body has been fully burnt.
The collected remains along with the ashes are put in a cloth which is tied around the neck of a person after some more ritual chanting and the said person is sent to Haridwar to scatter the ashes in Ganga. While heading to Haridwar, the person cannot re-enter the main village and has to leave directly from the cemetery via short cuts lying outside the village centre.
After reaching Haridwar, you contact with your designated hereditary priest who reads to you your entire family history and updates his record writing names of new family members who were born in the meantime. Thereafter you head to ganga where amidst vedic chanting the ashes are submitted to the mighty river and you are asked to take a bath.
For return journey you collect Ganga water in a bottle or any suitable container for home where after reaching more rituals in the temple follow before you are allowed back in the home.
Hindus observe the mourning for 12 days and on the final day a variety of customs and rituals are performed which are too long to be listed here.
That's all I can remember really.