They used artillery shells.

Early on they used large containers in front of their own trenches. When the win was at their back and blowing in the direction of the opposing trench, they would remove the lids and allow the gas to billow across no mans land.

Nope ... well, kind of. Gas was packed into grenades and artillery shells and loosed en masse and carried by the wind into enemy trenches.

As early as 1914, France used tear gas in rifle grenades. Germany deployed tear gas in 18,000 artillery shells on Jan. 3, 1915 at Bolimov, near Warsaw, in the first mass use of gas warfare. It was less than successful -- the gas froze and wasn't effective.

On April 22, 1915, Germany deployed 180 tons of chlorine gas at Ypres in the first large-scale use of lethal gas. German soldiers waited for days to get the right conditions. Then, they used wrenches to open tanks of chlorine gas and let the wind carry it to the Allied trenches. They shielded themselves with surgical masks soaked in chemicals and tore a three-mile-wide gap in the Allied lines.

Respirators, the prototypical masks that come to mind when you think WWI, were developed as a consequence, as were countless weapons designed to deliver gas: grenades, mortar shells, artillery shells, rifle grenades, chemical projectors. New gases were developed: phosgene, mustard, sulphur mustard, and more.

I used to work a job that specialized in dealing with left over munitions, so yay, something I can finally answer in depth!

They used all manner of munitions to deliver weaponized chemicals.

You have Stokes 4.2" chemical mortars, which were usually filled with mustard, enhanced mustard, or phosgene.

The Germans were especially partial to using chlorine gas, deployed from projectile shells (specifically favored were 155mm on the British side, and 15cm on the German side) or from large caliber mortars (usually 200mm mortars specifically were favored).

The British also used large mortars and projectiles. A weapon of special note is the Livens projector, which was almost like a mortar, but the propellant was separate from the projectile, which was itself designed more like a tank (think oxygen or propane tank) than a traditional shell. It was meant to impact on the ground with a burster and distribute a large amount of chemical agent everywhere.

Some grenades and rifle grenades were used, but they just weren't effective. They carried too little chemical, and the user had to be too close to the enemy and the poison for it to really be effective. (In WW2, the US did design some shoulder fired phosgene, 2.75" "bazooka" rounds, but those were never put into use.)

I don't know of any times gas was delivered by planes, but some one must have at least considered the idea, seeing that poison gas was originally developed from agents used in crop dusting.

You also have to realize that "mustard gas" isn't a gas for very long, and you aren't safe just by wearing a gas mask. After a shell explodes, the vaporized chemical quickly starts turning back into a liquid. That liquid then turns into puddles that lay on surfaces or get absorbed into the first layer of the ground. Mustard and derivatives are very insidious because they not only effect breathing, but cause boils on the skin. Those boils puff up and eventually break, leaking puss over the skin. That puss has residual mustard agent, which then creates more boils.

Because of that, once an area has been hit by mustard, or another similar agent, it becomes unusable land until it is extensively decontaminated (something they didn't have the luxury of on an active battlefield).

Another thing to realize is that chemical weapons are not always immediately visible. The image of giant white clouds doesn't apply to something like phosgene, so soldiers in a bombardment might not immediate realize they had been hit by chemical shells.

Another factoid is that gas masks do not allow for indefinite safety in a contaminated area. Eventually the filter breaks down (I don't know how long they lasted in WW1) and the mask becomes useless; this breakdown is even faster if the mask is exposed to a higher density of gas than it was designed for, and something like a trench environment, which naturally attracts heavy gases, is the perfect place for gas to overwhelm a mask. Some chemicals like chlorine also have the effect of displacing oxygen, which renders a mask useless, as it has no air to filter.

Sappers (explosives experts) were sometimes employed to place them and the explosive charge that would release the contents of the tank as well. All done under the cover of darkness and special operations of course.