Hi Pete and welcome back!
If you want to try your favourite old games, AmiKit is not the right tool for you. AmiKit, basically, is a heavily upgraded AmigaOS and its primary purpose is to run various programs, do a file-management, etc. Some newer games can be run easily too, but old games requires a special installer...
So if you managed to install AmiKit and you can see the desktop, you will need game files, usually in ADF format (one ADF file = image of one floppy disk. Many games consists of more disks). In AmiKit you can "insert" such a disk by doubleclicking the .adf file (it gets unpacked and inserted into virtual RAD: device). But like I said old games need special installer so they can be run on newer system like AmiKit. These installer can be found at www.whdload.de
Download and unpack the one you need, run it and the installer asks for the disks to be inserted... Use the .adf images like I described before.
However if you want to play games only, there's much more easier solution. It is called "Amiga Forever", a package that contains AmigaOS itself (required by AmiKit) together with a nice Windows player with many pre-installed games. It's really easy to run Amiga game with "Amiga Forever". Check it out at www.amigaforever.com