First, please note that Internet Explorer has been deprecated and replaced by Microsoft Edge since 2015. It is not known to be a secure browser and has frequent major vulnerabilities. If your service provider doesn't support any modern cross-platform browser (such as Mozilla Firefox or Google Chrome), it may be time for a change of provider or service.
That being said, if you really must use Internet Explorer and since it's only available on Windows OS you only have three choices :
- Use a Windows PC or install Windows on your Mac using Bootcamp
- Use a virtualization software (VirtualBox, Parallel Desktop or VMware Fusion) to run Windows inside a virtual machine on macOS
- Use a compatibility layer to run windows programs on macOS without virtualization
That last choice may be a good alternative if you only want to run one specific program and don't need a full-fledged Windows running. Wine is a free and open-source solution capable of running windows program on Unix-like systems (Linux or macOS).
You can install and setup Wine manually but it's mostly dedicated for advanced system administrators. However, there are multiple packaged front-ends for Wine that allow running windows program on macOS without much technical knowledge :
- PlayOnMac, the Mac version of PlayOnLinux, is a free software and provides a user-friendly graphical interface with configuration templates to run the windows version of Internet Explorer
- CrossOver, a commercial solution with customer support if you have some money to spend. It also provides a graphical interface and may have better support than PlayOnMac.
- Winetricks, another open-source solution but mostly dedicated to advanced users
Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, possibly no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may still be the easier way to go.
FYI, I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :
It may very well be the best solution if PlayOnMac doesn't work and you don't have the technical background necessary to setup Wine manually and you don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.