The first thing to keep in mind is that there is no one turbulence model that works well in all situations. You need to choose the right model for the right situation. See this link for reference: https://engineering.stackexchange.com/questions/336/which-turbulence-models-are-suitable-for-cfd-analysis-on-a-streamlined-vehicle-b/344#344
There are many types of models, all with varying degrees of accuracy and computational cost. Generally speaking: the more accurate the model is, the more computational cost it incurs. So you need to consider very carefully how much computational expense you can afford versus how much accuracy you really need.
With that said, it is not trivial to convert laminar code to one that handles turbulence. Depending on the model, you may need up to 7 additional variables and equations, and heuristics to specify these new values at the boundaries.
Depending on whether you're considering compressible or incompressible flow, you may need to modify your momentum and energy equations with additional terms which include these new variables, along with varying expressions for the turbulent viscosity and turbulent Prandtl number.
My recommendation: have a look at OpenFoam, an open source cfd solver with lots of turbulence models already implemented. You can get a good idea of how to modify your code from this (assuming your solver uses finite volume method).
Admittedly, OpenFoam has a steep learning curve and may take a while to master navigating it. But I think this is your best bet when it comes to learning implementation of generalized cfd code.