To Osaka then Fukuoka from Tokyo

What is the best way to travel to Osaka then to Fukuoka from Tokyo for example by air,bullet train,and the costs

buy a JR pass

Its one of those many variable question and answer situations.
EG by Hikari to Shinosaka and then a local to Osaka can be done in 3 1/4 hours for Y13750.
By plane and all the various connections it takes....3 1/4 hours for Y23840 but you would get a much better fare off a discount travel agent or airline. So there is no time difference and there may well be no price difference but getting the plane would be a great deal more of a drama. Now if you go by Nozomi ( that is no JR pass ) you can knock 20' off but pay Y14050.
From Osaka to Fukuoka a Nozomi or Hikari Railstar beats the plane timewise ( under 3 hours for Y 14590/14890 ) and I would suggest farewise ( around Y22000/23000 all up for the plane ) unless you can get a great deal on the plane.
If it were me I'd use the train and if you are doing it within a 7 day period it may be well worth getting a 7 day JR pass at Y28300 you break even and have the option of using it for other trips. You just don't get on the Nozomi with it.

We recently took the overnight ferry from Osaka to Fukuoka and it was a great experience and very economical considering hotel and transport were one fare.