Assuming your own data is in proper format, the process is to start by calculating the data in a format in which the isotherm is linearized for better fitting quality and then apply a linear fit in your preferred software (Excel/Origin/...).
The linearized functions for the standard isotherms Langmuir, Freundlich and BET can e.g. be seen in fig. 5 here:
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You can follow Langmuir, Friendluich & Temkin model for batch adsorption,,, but for column adsorption you can apply Thomas, Yoon Nelson, Adam bohart, clark model, etc