The standard method for transferring files between Macs is to use a USB drive, or conventional file-sharing services via network connections, though these days the use of synchronization services like BitTorrent Sync, Dropbox, and Google Drive offer progressively reliable alternatives. When using standard file sharing, you should be able to log in to the system and see your hard drives and home folder as share points for reading and writing files.
However, sometimes an odd snafu or two may prevent these services from working. If you find yourself unable to log in to your system and mount a shared folder, you can try logically "jiggling" your system by restarting and disabling or re-enabling file-sharing services.
But if this doesn't work, one way to at least get your file transferred is to use Mac Screen Sharing services. Even though screen sharing is primarily used for remote desktop services, it also supports file transfers.
To do this, you need to have Remote Management enabled in the Sharing system preferences, which I highly recommend keeping enabled as an avenue for workarounds and troubleshooting, provided you have more than one computer available.
With Remote Management enabled on the target system, a "Share Screen..." button will appear when you select the system in the Finder sidebar or if you browse the Network located at the top level of your system in the Finder and open the shared computer located in there.
Once a Screen Sharing session is established, you can resize the window to make it fit on your screen (the shared screen may scale proportionally), and then you can drag files from your current system to a location in the shared screen session to copy files, or copy and paste to place the files.
When you do this, a small File Transfers window will pop up showing the progress of the download and any additional transfers you initiate or have completed. During the transfer, files will be saved in a temporary folder structure called "ssdownload," in which there will be numbered subdirectories containing the active transfers. Once completed, the transfers will be copied out of this folder structure and the structure will be deleted.