To attach to an existing process in x64dbg, select File | Attach (or Alt + A); this will bring up a dialog displaying the running processes, as follows. Choose the process that you wish to debug and click on the Attach button. When the debugger is attached, the process is suspended, giving you time to set breakpoints and inspect the process's resources. When you close the debugger, the attached process will terminate. If you do not want the attached process to terminate, you can detach a process by selecting File | Detach (Ctrl + Alt + F2); this ensures that the attached process is not terminated when you close the debugger:
Sometimes, when you try attaching the debugger to a process, you will find that not all of the processes are listed in the dialog. In that case, make sure that you are running the debugger as an administrator; you need to enable the debug privilege settings by selecting Options | Preferences and, in the Engine tab, checking the Enable Debug Privilege option.