You're right, you will have to transfer the files to the new partition before mounting it, as /home to use an example. This may seem like a hazzle but I think it's worth it in the long run since you can easily backup or move the /home directory to another hard drive if needed. It is considered "good practice".
When installing Debian you must have at least a root partition and a swap partition - this probably goes without saying. But you're right about the installer not being very talkative about the options.
If you have created more partitions with the Linux partition type you will have the options to "Initialize another partition" and after that "Mount another partition", but they are not the default choices (you have to hit the down key a couple of times to see that option, perhaps?). You must first mount the root partition though.
When you choose to mount this initialized or not initialized partition you will get the question on where to mount it, and the installer describes briefly the purposes of different mount points - /usr for all software, /home for user homes, /var for things that change a lot like web content, mail and logs.
Initialization means formatting the partition (which creates a filesystem and removes all data on it) so it might be wise not to do that if you're mounting a backup partition.
It's been a while since I installed Debian (you usually only do that once on a computer) so I'm not 100% sure of the language used in the installer or the exact sequence of things, but I hope you get the general idea.