As explained here, systems science "builds on the calculating capacities of digital machines. It counts on the possibility to enhance our attentiveness and awareness for the consequences of interactions with the addition of computational power." That's why studying systems science has to include the acquisition of at least basic computer literacy.
Many modeling platforms - like the point-and-click methodologies of the System Dynamics platform Vensim or of the proprietary agent-based platform Anylogic for instance - allow to construct complex models with no or with little programming skills. Others - like the modeling environment Netlogo - operate with easy-to-learn programming languages, but restrict their use to the particular needs of agent-based modeling. However, for being able to transform data into appropriate form for analysis for instance, or for building more complex models and performing statistical tests or parameter runs on them, it seems highly advisable to know at least one higher-level programming language. A good choice in this respect seems to be Python.
Python is a programming language that - according to its webpage - "lets you work quickly and integrate systems more effectively". Its currently about to become one of the most widely deployed programming languages in scientific computing.
A good way to start learning Python is the Code-academy. Alternatively, you can try the Beginners Guide to Python which also covers topics like how to install Python on your computer. Or you'll try to Learn Python the hard way.
The maybe most convenient way to deploy Python is via the IPython-Notebook which is a browser-based interactive computational environment that allows to combine code execution, text, mathematics, plots and rich media into a single document (the Python-code in this etextbook - as for example here - makes use of IPython-Notebook). The IPython-Notebook runs in your browser and does not need any additional compiler or integrated developer environment (IDE). It can be obtained for free with the Python distribution Anaconda which - according to its webpage, is a "completely free enterprise-ready Python distribution for large-scale data processing, predictive analytics, and scientific computing"
A big advantage of Python is the availability of many specialized open source libraries which add functionality to your code. Many of these libraries are readily included into Anaconda. So installing Anaconda will give you access to the IPython-Notebook and to most Python libraries that you'll need for a start.