To begin downloading Inkscape, go to Inkscape.org:
Click on the Downloads drop-down.
Then click on your current Operating System's image. Linux, Windows, and MacOS respectively.
For Windows users:
Select the proper version of Windows that you have, either 32-bit or 64-bit.
If you're unsure, download and install the 32-bit version.
For Mac Users:
Click the image to start downloading Inkscape, then follow the step-by-step instructions on running Inkscape on your MacOS, which includes ensuring you have XQuartz installed.
For Linux users:
Select the proper download from the options presented.
For Windows Users, open the .MSI file you downloaded.
After accepting the Agreement, you can choose which Install you want.
If you're unsure, just choose Typical.
Then just click Install.
When it finishes installing, you can then click Finish to get started!