Thanks to the conda-forge community, geopandas
is actually pretty easy to install on all platforms using the conda package manager (or: its dependencies, as this is the difficulty).
If you have conda, it is just:
conda install -c conda-forge geopandas
To install conda, you can install the Anaconda python distribution or miniconda: http://conda.pydata.org/docs/download.html
See the GeoPandas docs for more details, specifically on how to create a new environment with GeoPandas installed with settings to ensure this always works: https://geopandas.org/install.html#creating-a-new-environment