Wireless printer

[#1]

I have just  purchased a hp Deskjet F4580 wireless Printer, and have run in to trouble trying to instal the software( my ignorence)
Ihave selected the wireless option and have been asked for a network name or some thing ( i'm afraid I can't remember exactly and didn't write it down. I don' t know of the required name , but, It has got me thinking, do you have to have a wireless router in order to be able to do wireless printing.?  I have a wired router.
Thanking you in advance.
[Moderator's note by Thomas (Be3G): thread moved to a more appropriate board.]

[#2]

Yes.
And even if you do have a wireless router it's (much, much) easier to set it up wired first then change to wireless.
Basically the printer, in wireless mode, talks via the router, NOT directly to the PC.
(though I guess a techie like me could make it work that way) 

[#3]

Many thanks for your reply.
This is the 5th hp printer that I have had & never had any trouble setting them up until now .
Having said that, this is the first all in one that I have had.
Ihave allready decided to un install an re- install  as wired, but for some reason it's giving me trouble .
It said installation sucessfull , but when I tried printing after ligning it up , all I got was plain paper coming through, yet it printed on ligning up .
Beginning to wish I had never bought an all in one. 

[#4]

Apparently , the device driver software was not successfully installed for some reason, so re-installed and all is now fine.
I was baffled for a while though. I went to print my Plusnet Invoice and nothing happened .
Went in to works  & tried printing both text and a picture & both printed as quick as you like.
I then suddenly realised why my invoice wouldn't print . The Plusnet website doesn't like 64bit .
Tried 32bit & bingo
Many thanks for your help.