Engine light is on, car sputters when I accelerate on the gas. How do I fix carbon buildup my self

There are 3 steps to take when cleaning up carb build up. Fuel injector cleaning (done with a fuel additive), throttle body cleaning (with a throttle body cleaner) and an intake cleaning (with a bottle of intake cleaner through a vacuum port with the engine running). A shop will generally perform this 3 part service for around $70-$150 depending where you go. More than likely it will be more cost effective to go through a shop, the service is generally guaranteed, and if there is another problem, the service adviser will typically suggest a better course of action to rectify the check engine light and sputter. Kind of strange that there would be a check engine light but no present or stored codes for something like this.