If you’re new to Grosh, just download the app and tap “Got invitation code?” on the last intro screen. This will take you to the Settings screen in the app, which lets you enter your name, email and the invitation code. Note that the code is only valid for 48 hours, after that your friend needs to re-invite you.
If you are already using Grosh, tap Menu-Select list and tap the + button to enter the invitation code.