Attach a LUN from the new SAN as a new drive on the machine that runs SQL Server.
Stop the SQL Service, and set it to Manual so that it won't accidentally restart.
Copy the MDF and LDF files to the new drive/SAN. Be sure to preserve all folders, etc.
Swap the disk drive letters between the new and the old SAN drives (effectively swapping the drives).
Manually restart the SQL Service.
Check everywhere you can think for error messages. Check again. Ask someone else to verify that things are clean so far.
Start using your applications, be very careful to see that they work as expected.
Once you get to this point, the old SAN drives are just excess baggage. They allow you a "fallback to before the switch" just in case anything goes wrong. Once you are comfortable, you can disconnect them from the SQL Server machine.
In theory, theory and practice are identical. In practice, theory and practice are unrelated.