If I understand correctly, you turn on the computer and drive, the system stabilizes and then you attempt to read floppies. I also assume you have the drive cabled correctly to the computer. The 1541-II is just like a 1541 except that it's smaller, probably a little faster, and you can change the drive assignment with the switches on the back.
The switches on the back should be in the up position for drive 8, the default drive for a C64 software.
after you've confirmed the switches are both up, try
How to get a disk directory:
LOAD "$",8 [return] - if there are any files on the disk it will still say "loading, but when the drive lights go out, rather than type RUN, type LIST to get a directory of the diskette.
NOTE: each time you fail to get a disk directory to appear on the screen, it's best to power down everything wait 3 seconds and power everything back up again. There are other ways to re-initialize a system but for now just do that.
If after you try a number of disks that appear to have data on them yet nothing useful comes to the screen you should next try to format a diskette. Formatting a disk often fixes minor problems and make shake the heads free if they're stuck.
Insert a disk you don't care about getting overwritten into the drive. type the following command:
PRINT#15, "NEW:mydisk,01" [return]
Watch the disk lights. If you listen closely you can hear a click click click as each track is formatted. When the process is done (it will take a minute or two), power cycle the computer and try the disk directory command above on this disk. It will be blank, but you'll see "mydisk 01" on the screen more or less. You might find that now you can read other disks too.
Let us know how that goes.
Bill