You can use pip install, conda, or Anaconda3 to install Fiona:

>> conda install -c conda-forge fiona
>> conda install -c conda-forge/label/broken fiona
>> pip install fiona

Fiona requires Python 2.6, 2.7, 3.3, or 3.4 and GDAL/OGR 1.8+. Fiona depends on the modules six, cligj, munch, argparse, and ordereddict (the two latter modules are standard in Python 2.7+).

Consult Fiona's readme page for more download info https://toblerity.org/fiona/README.html.