How to climb Mount Fuji departing from Hakone

I would like to climb mount fuji and visit Hakone.

I was planning on going from Tokyo to Hakone and stay 1 night in Hakone.
The next day I would like to climb mt Fuji.

How can i get to mount fuji from Hakone? What buses/trains should I take & how long would it take/ what�fs the price.

Or should I plan both (Hakone & climbing mount fuji) as a day trip from Tokyo?

Thanks in advance