Is it one of the 5 1/4" disks? Then, label facing up, oval window at the bottom of the disk going in first, so that that oval ends up deep into the drive with the label most likely under your thumb, as it were. If there is a write-protect tab clipped out, that should be to the left.
Sometimes the disks are double-sided, in which you could use both sides, but that was not recommended if I remember rightly. I still did it, though... but I kept two copies of things.
I don't have a picture handy, but I hope this gets the idea across.
You are right, if it just spins, then it either might not have any data, or there might be an issue with the drive or disk.
If I recall, if you start up the Apple without a disk, then you only get some basic Applesoft (BASIC) prompt; in order to run any programs that access the floppy drive, you need to load either a program disk or an Operating System. The last one I used was DOS 3.3; I never worked with PRODOS but that is another option.
I don't know what the copyright issues are these days, but I think there were FTP sites from Apple where you could get DOS disks. I don't remember where they were, it was a long time ago, but I can look...
There are several sites that have disk images available for download. And there are a couple of different ways to get them down to your Apple. But if it turns out you don't have a viable DOS diskette any more, you'll want to take a look at bootstrapping instructions here: http://adtpro.sourceforge.net/bootstrap.html
I am sorry, I can't find it right now.. haven't looked for it in a long time (my Apple II use is on hold...) but I can try again... I just can't find it tonight.
There are several sites that have disk images available for download. And there are a couple of different ways to get them down to your Apple. But if it turns out you don't have a viable DOS diskette any more, you'll want to take a look at bootstrapping instructions here: http://adtpro.sourceforge.net/bootstrap.html