With the Ruby in your inventory, go to the House of the Hero at (G-3) in Windurst Walls (fastest to take Home Point #1 warp; if you don't have this, then exit Windurst Waters and go East/North). Check the front door for a cutscene, where you will be asked to find "the seven colors".
The "seven colors" that are required correspond to the colors of a rainbow. They are obtained by zoning into an outdoor, enemy-populated area while one of six weather effects is active—the seventh is obtained by zoning into an outdoor, enemy-populated area with no weather effect at all.
To clarify: "Outdoor" means that you may not zone into a cave or dungeon area to obtain a color.
To clarify: "Enemy-Populated" means that you may not zone into a town or city to obtain a color.
Cannot obtain weather effects by having Scholar cast them on you.
Zoning into an area with the above requirements (that you have not yet obtained) and with the ruby in your inventory (Mog Satchel and Mog Sack as well, but not in your Mog Case) triggers a short cutscene upon entering the area, where Carbuncle will remark on the color of light that you have found. You will not see the same cutscene again.
This can be done by logging out and back into the zone.
This can be done while riding a chocobo.
This can be done by using an outpost teleport into the zone.
This can be done by teleporting into the zone (Teleport-Dem, etc).
You can zone into an area under Monstrosity and still receive the weather cutscene and credit. See Odyssean Passage for a list of applicale areas.
Weather CheckerNPCs in each town or city can help predict when and where the weather you will be looking for will be in effect. Bear in mind, however, that these Weather Checkers are not completely accurate; some weather effects may occur on days they are not forecasted, and vice-versa.
Each time that a player completes this quest, a rainbow (the same one as seen in the cutscene) appears over the Crag of Holla on the next Vana'diel day (so long as the weather is not rain). Should it be rainy weather, the rainbow should appear shortly after the rainy weather stops if it is before 18:00 in-game. The rainbow will appear the same Vana'diel day if you complete the summoner quest early enough in the game day.
Even if a possible weather is not predicted by a Weather Reporter, there is still a slight chance that it can occur, if the day corresponds to that weather.
Vana'diel has Seasons which affect the weather. If you are having trouble finding weather it may be the wrong time of year.
Outdoor, enemy-populated areas, that have the weather elements but will not react to the quest:
Qufim Island (To get the weather for this location you must enter Qufim by exiting Lower Delkfutt's Tower)