I had the problem, that Rider did not install Unity plugin automatically into the project as it should.
At the moment I have installed Rider JetBrains Rider 2018.1.1 Build #RD-181.4952.276
and Unity 2018.1.0f2
First, in Unity check the Preferences ( Menu -> Edit -> Preferences ) there External Tools, set External Script Editor to rider.sh which you will find in your $HOME/bin usually.
Open your project in Unity, and thereafter in Rider. - maybe try this two times. If Rider does not install the Unity Editor Plugin, you can do that yourself also.
Search in your rider installation for the file JetBrains.Rider.Unity.Editor.Plugin.Repacked.dll
find . -name JetBrains.Rider.Unity.Editor.Plugin.Repacked.dll
Output for me is
./.local/share/JetBrains/Toolbox/apps/Rider/ch-0/181.4952.276/plugins/rider-unity/EditorPlugin/JetBrains.Rider.Unity.Editor.Plugin.Repacked.dll
Into your Unity Project go to the Assets Folder and create the directory Plugins/Editor/JetBrains
e.g. assuming your project is in the relative directory dev/myunityproject , the command line would be
mkdir -p dev/myunityproject/Assets/Plugins/Editor/JetBrains
Copy the plugin to the newly created folder
cp ./.local/share/JetBrains/Toolbox/apps/Rider/ch-0/181.4952.276/plugins/rider-unity/EditorPlugin/JetBrains.Rider.Unity.Editor.Plugin.Repacked.dll dev/myunityproject/Assets/Plugins/Editor/JetBrains
Reopen Unity.
Check in rider if the unity support plugin loaded in editor and connected to unity.
Links
https://github.com/JetBrains/resharper-unity/blob/wave12/readme.md#unity-editor-plugin
https://www.jetbrains.com/help/rider/Unity.html
https://blog.jetbrains.com/dotnet/2018/04/05/control-unity-editor-play-mode-rider-2018-1/