Location

Gas clouds are found inside wormholes and K-Space in low sec and null sec. They are only found very rarely in high sec and then only via Exploration.

Skills needed

To mine a gas cloud you will need the skill Gas Cloud Harvesting. The skill book currently runs 21.6M isk, and is available from all normal NPC sellers.
To learn the Gas Cloud Harvesting skill you need Mining at level 4.
You can only install one gas cloud harvester per trained skill level. Note that this is very different from normal mining, where you can fit one mining laser per turret slot.
If you're going to invest in this skill, consider training it to level 5 at once, because the harvesting rate of 5 T2 harvesters is almost double that of 4 T1 harvesters.

You will need a ship that has enough high slot turrets.
Unlike other mining, gas cloud mining can not be performed in any type of exhumer. (They can not mount high slot turrets.)
You will also need at least one Gas Cloud Harvester. You can only mount one harvester per trained skill level, and each one uses a turret slot. A battlecruiser works nicely for this, or a cruiser with 5 turret slots such as a Thorax.
Unlike regular mining, there are no gas equivalents to the Mining Laser Upgrade.
You'll probably want to fit some cargohold expanders as well -- gas is bulky. A
A ship with gas harvesters attached appears to have nozzles coming from the body of the ship. The number of nozzles does not necessarily match the number of gas harvesters fitted.

To be able to target a gas cloud you need it selected to display on your overview.
To do this, right click the overview, select open overview settings, select the filter tab, open the celestials folder, and check the Harvestable Clouds box.

Move within 1500m of the harvestable cloud (the range of a Gas Cloud Harvester 1 module).
And start your harvesters. Note that unlike regular mining, there's no pretty visual effect. The gas just appears in your cargo hold.

With a Gas Cloud Harvester 1 you will receive 10m3 (1 unit) of gas per 30 seconds (1 cycle). T2 harvesters are faster, yielding 20 m3 every 40 seconds.
At 10m3 each it does not take a lot of gas to fill most ships' cargo holds.

Notice this is just for high sec gas and is not the same for low and null sec gas.

Gas from gas cloud sites is used in the manufacture of Boosters.
Gas from wormholes is not used in booster production but instead is used in T3 manufacturing. This can be extremely profitable.
Gas from high sec exploration sites is of the Mykoserocin variety, these produce the basic synth boosters.
Synth boosters are NOT illegal and have no possible side effects.

Other gases from low and null sec make higher grades of boosters that are illegal and have "possible" side effects.
On these boosters you are guaranteed the good effect, but there are 4 "possible" bad side effects. (You may get none, you may get all 4; there is a percent chance for each side effect.)

See Also Exploration sites : Ladar
See Also Boosters
(Special Thanks to Artemeo for finding a ladar site in high sec, that allowed the pictures on this page.)