Is it like android where you can just get an apk installer program, and download apk's for linux? Or is that an android specific thing? I've had a few linux OS's in the past, but I only ever used the snyaptic package manager or whatever was built in.
No. APKs are specifically for Android, and won't work for Linux.
It depends on the program itself on Linux. Sometimes you have like a .deb file whereas you can install easily like on .exe files on Windows systems, but sometimes you have to use batch commands to install that certain program and other pre-requisites.