Wouldn't fusion use up the worlds oceans relatively quickly?
No.
The thing is, fusion reactions release a lot more energy per reaction than fission reactions.
Also, normal one-proton hydrogen is all but useless for (first-gen) fusion technology, so most of the water will not be used at all. The reactors will be using deuterium, which is present in heavy water, and tritium, which can be obtained from Lithium-6 or Lithium-7 by bombarding them with neutrons.
And, as deuterium-tritium-reaction results in helium-4, a neutron and energy, it's possible to simply cover the insides of the reactor with lithium in order to create the needed tritium. And, as lithium is the 33rd most abundant material on Earth, there'll be a long time until we risk running out of that stuff. So even using deuterium from the oceans and tritium bred from lithium, the fuel reserves would last estimated hundreds of thousands years IIRC.
Furthermore, it's estimated that deuterium+tritium->helium+neutron -reaction will likely be used in the first gen fusion reactors because it is one of the easiest to achieve. In the future, deuterium+deuterium is probably possible to achieve - it produces less neutrons than D+T-reaction, which is good, because neutron flux makes the reactor structure radioactive and lessens the amount of easily collectable energy from the reaction. Charged particles' energy can be converted more directly to electricity than neutrons' energy.
There are also more possibilities on fusion reactions, which are more difficult to achieve, but as the engineering advances, they should become available, and thus they'll give even wider range of fusion fuel to use. And that means that when the fusion power becomes widely available, it will not run out of fuel any time soon.
