To please Ra, you must light seven bonfires, each containing at least 7000 wood, around a Spirit Brasier; burn five spirits of a particular type in the brasier; and sacrifice an ambrosia of flavored wine and dates at the brasier.
Next, there needs to be seven bonfires each containing at least 7000 wood. Obtaining that much wood will probably be a group effort. The recommendation is that that each bonfire contain sufficiently more than 7000 wood, depending on how many people are using the brasier during a given festival. The bottom line is that all bonfires must never be allowed to burn down to less than 7000 wood while anyone is still sacrificing their ambrosia. Bring along some water and heavily douse the fires so they burn much slower. Once everyone has sacrificed their ambrosias, tear down the bonfires to re-use as much wood as possible.
Check this page for a list of locations that have been prepared for Ra festivals.
Next, get 5 spirits of whatever type you need. Though there are many types of spirits that can be made, Ra only seems to ask for Mineral, Fruit, Grain, and Wood Spirits. Note that if your requirement is for Fruit Spirits of Earth, you should do a different festival to reset your requirements -- while they are not technically impossible to distill, no-one has ever done it ;)
Finally, find your wine and make wine/date ambrosia. In addition to being your randomly selected flavor, the wine must be at least two vintages old and contain at least 10% alcohol. Like the beers in other festival types, the wine may contain extra flavors. For example, "Cherry Apple Raspberry" wine would satisfy a "Cherry" requirement. 10% alcohol means that the wine has to be made with grapes that have at least 10 Residual Sugar. Those grapes must ferment long enough to convert the sugar into 10% alcohol. Vintage refers to the in-game season during which the grapes were harvested. The vintage seems to change roughly every 10 real-life days (more study is needed to ultimately define when a vintage changes). Basically, the grapes must have been harvested over 20 days ago, have contained at least 10 residual sugar at time of harvest, and been fermented long enough to reach 10% alcohol. See the Wine pages for more information.
Try the Wine Inventory to find a supplier for your wine and the Spirit Inventory to find a supplier for your spirits.
See also: The Test of Festivals, Determining Festival Requirements, Festival Altars, Festival Schedule, Festival Needs, Possible Wines and Spirits.