F# (Windows) - Easiest way to install latest versions of F# on Windows is using VS Build Tools 2017. If you use VS 2017, make sure that you've installed workload adding F# support.
F# (Linux/MacOS) - F# on non-Windows platform is distributed as part of the mono. Installation guide and recent version of mono can be found on the project webpage and on the F# Software Foundation "Use on Linux" page
.NET Core SDK - .NET Core is modern, cross-platform implementation of .NET Framework. Ionide is requiring it for set of features such as project modifications or debugging. The core part of SDK is dotnet CLI tool that provides easy way to create, build and run F# projects. What's important - the dotnet tool can be used also to create applications targeting also Full Framework (like net461). For detailed instructions on installing .NET Core, visit official step-by-step installation guide.
MSBuild 2015 (Windows only, optional) - For old, verbose .fsproj files on Windows MSBuild 2015 (14.0) needs to be additionally installed. You can download it here. However, we highly recommend using new, SDK-based project files.