The keep nearest each gate must be captured to trigger the opening of that gate.

It can be quite hard to catch those enemy gates open.

Just to add to the above, the two controlling keeps-- the one closest to a given gate, and the "linchpin" keep which is between the two gate keeps-- do not need to be the same color; they just need to be different than the color of the gate.

Thus, to open a yellow (AD) gate, the two controlling keeps need to be either both blue (DC), both red (EP), or one of each.

To open a blue gate, the two controlling keeps need to be both yellow, both red, or one of each.

To open a red gate, the two controlling keeps need to be both yellow, both blue, or one of each.

The alliance which owns the two gates will usually fight like crazy to prevent the controlling keeps from being captured, and to reclaim them if they've been captured, so it can be difficult to find the gates already opened up, or to successfully open one up and keep it open long enough to go through the gate and grab the skyshard behind it.

Fortunately, there are a few tips that can help you collect all of the skyshards in Cyrodiil.

If at least one of your characters has collected all of the skyshards in a given zone, those skyshards will become unlocked in the Crown Store and can be purchased as a pack on any other character who doesn't have them yet. Cyrodiil is a large zone, divided into three territories by natural terrain and walls, with each territory being home to a given alliance, and the Cyrodiil skyshards are available as three separate packs in the Crown Store, one for each alliance territory. One way to collect all of the Cyrodiil skyshards on all of your characters is to make at least three characters-- one in each alliance-- have them collect all of the Cyrodiil skyshards which are in their alliances' home territories, and purchase one or more of the Cyrodiil skyshard packs as needed on your characters to get whichever skyshards are otherwise unobtainable.

You can also collect them all on a single character by purchasing and using alliance-change tokens so you can more easily collect the skyshards which are behind any alliance gates you haven't otherwise been able to get through.

If you don't want to spend Crowns on skyshard packs and/or alliance-change tokens, and prefer to wait until the necessary gates have been opened up through warfare, you can check the map of Cyrodiil on a frequent basis to see when those gates happen to be open, then queue into Cyrodiil and make haste to the appropriate gates to collect the skyshards behind them. Note that if you aren't in Cyrodiil, looking at the map of Cyrodiil will show you the current map for your home campaign. If you haven't chosen a home campaign, or want to view the map for some other campaign, you will need to actually queue into a given Cyrodiil campaign to see what its map looks like.

It sometimes happens that each campaign becomes dominated by a different alliance, so check the maps for all campaigns to see if the gates you need to get through are opened up on any of the campaigns. It doesn't matter (as far as getting inside the gates) whether the controlling keeps have been captured by your character's alliance or the other enemy alliance, so don't avoid a campaign just because the map is dominated by an enemy alliance.

And as far as actually getting through an opened gate, you don't need to fight and kill the guards protecting it-- it's usually a lot simpler, and faster, to just mount up and ride as quickly as possible past the guards and through the gate. Once you get far enough past them, they won't chase after you.

If the alliance which owns the gate manages to recapture one or both of its controlling keeps, such that the gate closes while you are inside, you can get out again (after collecting the skyshard) by climbing the stairs and jumping over the gate wall-- or you can just queue for one of the Imperial City campaigns.

Agree with checking the various campaigns periodically to see if the gates are open. Check at different times of day, and different days of the week. Having the announcements turned on helps here (and turn them off once you get the skyshards, so annoying).
I got those skyshards in Ravenwatch back when I needed them.

I'm worried about this tactic if/when we lose the quiet campaigns to Greyhost/Vengeance only.

I logged in no alliance bond mode. So, I didn't meet other player except 2 yellow players.

Simply lonely Cyrodiil situation. So I want to find solo solution for this...If I can.