There are some current issues currently recognized today as having significance to the planet's climate. (I am avoiding getting into any political discussions here about climate change, so i will keep my language as neutral and non-political as possible.)
You could make up a global warming theory, based partially on current discussions and partially using literary license, to create a plausible scenario.
For instance- there is discussion about the relationship of polar ice and the global temperature. Ice reflects solar heat into outer space; conversely, water is darker and absorbs more heat. More heat would cause more ice to melt, which increases the heat absorbtion etc. In theory this could be a runaway cycle.
What if all the polar ice would melt at one time? Say a massive volcano would erupt right at the north pole, spewing tons of molten lava all over the ice cap. This would melt lots of ice and raise the temperature right away (from the heat of the lava), as well as causing more solar energy to be absorbed in the future. You could substitute a meteor crashing into the North Pole as well, or any other sudden traumatic incident which would destroy the polar ice cap.
Now this by itself isn't enough. All this would do is raise the temperature of the planet, cause more water to enter the atmosphere and at best create a humid greenhouse. It might devastate planet earth, but it wouldn't turn it into a desert because the moisture would stay trapped in the atmosphere. So eventually it would rain back down again. And, as the planet's climate works in cycles, it probably would eventually completely recover its ice covering as well within a few thousand years.
You need a mechanism to turn the atmosphere dry.
Here again, we have a contemporary issues which could be borrowed and adapted for your purposes: the Ozone Hole.
The ozone layer is made up of a type of oxygen molecule, found naturally in the atmosphere. It absorbs lots of radiation from outer space. As the ozone layer gets depleted, it allows more radiation to reach earth.
This helps your story in a couple of ways. First off, the extra radiation will help speed up the warming and prevent the ice from reforming.
Second, the hole could be used to explain how Earth could lose the moisture. You could have a form of radiation which could react with water and break it into hydrogen and oxygen, with the hydrogen then leaving into outer space.
Or, with some more literary license, you could just make the atmosphere leave via the hole. The heat and added moisture creates such pressure that it presses the moisture-laden air out into outerspace.
Either way, this gives you a situation where the Earth is heating up and the ocean water is evaporated, but ends up escaping into outerspace instead of raining back down to Earth. You could thus conceivably make a time frame of a couple hundred years for Earth to look similar to Mars. (It wouldn't be anywhere near identical to Mars yet, but it would start to be comparable and would already have devastated life on Earth.)
To keep the ozone hole from healing itself, you would want to include a natural volume of certain chemicals like chlorine, bromine, nitric oxide etc. As radicals, they interact with the ozone layer and keep breaking apart the oxygen moecules, thus furthering destabling it. So for example, maybe mankind discovers that as the polar ice melts, a natural deposit of bromine is uncovered. This bromine reacts with the ultraviolet light (which hits earth stronger because of the ozone hole) and release bromine radicals, which then continue to enlarge the ozone hole.
Again, this is not strictly scientifically accurate, but it could work as a pseudo-scientific explanation and could be plausible to the reader.