If that all sounds really complicated, don't worry about it. In order to create a new photosynth, you just use the Photosynth app for Windows.
You can launch this with the shortcut to the program in your Start menu with all your other programs. If you like, you can copy the shortcut to the app from your Start menu to your desktop.
If you have Windows Vista or above, you should be able to just search your Start menu with the built in search bar and the app's shortcut should pop right up.
If you can't find the shortcut but you know you have installed Photosynth's program on this computer, you could check in your 'Program Files' folder to make sure that the Photosynth app's folder is there. If it is, click on PSWebClient.exe and the app should open.
To make opening the app easier in the future, you can right click on PSWebClient.exe and select the 'Create a shortcut' option. Then drag that shortcut to either your Start Menu or Desktop folder.