PlayStation Network is not down. If you're getting an error code when you try to sign in please note the number down and type the error code in the PlayStation Knowledge Centers Error Code search. This can be found on the top right hand side of the page. Link below.
If you can't figure out the problem after you read on your error, please don't be afraid to disclose the error code here. I hope this helps.
NOTE: You can always contact the PlayStation Knowledge Center. They have a live chat now. Link below.