Games autoboot. The ones that don't will autoboot TownsOS, then you select the icon. Most games boot from CD, a few come with special boot floppies. However if you don't have compatible hardware the games will not boot. For example a lot of the RPGs require a keyboard, if it's not plugged in, no boot. Same for games that require a mouse. Also games that require floppy disks often won't boot if they can't read the floppy drive, or don't find a compatible disk. Some games require you to format the floppy disk yourself before booting, others just need any disk inserted.
To test your floppy drive, simply go into the system menu and attempt to format a floppy. And in the end, even if you have everything, the games might not be Marty compatible, as I told you before, the Marty is a piece of shit. It's alright for some of the older arcade ports, but for RPGs and more advanced games it is extremely limited.
Just about every "Marty compatible" list I've seen on the internet has errors. Unless the game has the Marty logo on it, it's pure luck if it works or not.