How can we produce diesel out of old trashed out tires??

Pyrolysis or gasification is a way of turning waste materials into condensable and non-condensable vapors (smoke). These non-condensable vapors can be burned as "producer gas" for energy/heat/electricity.

 

The condensable vapors can be cooled, collected, and refined to create bio-oil, a liquid fuel; as well as other commercially viable products such as vinegar or organic acids.

 

But it is usually not economically viable. There are ways of combining these processes with other commercial or social or humanitarian projects to make it more viable, but it's no big moneymaker... so far. If you've got some new ideas about how to make the separation or fractionation or the refining easier, you could make the world a much better place; so feel free to share.

 

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I think you would also have to trap the sulphur compounds before you burned the stuff of the SO2 produced would contribute to pollution and acid rain.

People do recover isoprene from used tyres. I'd guess isoprene is a molecule small enough to separate well from sulphur, this avoiding the real hurdle.

 

Once you have isoprene, you can make pretty much anything of it, including new rubber, better replacements for Diesel oil, kerosene, rocket fuel (I contemplate Farnesane and Phytane here)...

 

The real difficulty is that latex is a very cheap source of isoprene, and paper factories offer terpenoids nearly for free as by-products (turpentine, pinene, carene, pinane, myrcene...). Crude and refined oil are also dirt-cheap, though they're getting expensive for the uses we make of. So a material from tyre recycling would face very hard competitors.