How to go on invalid area of each JR-pass

How to go to invalid route of each JR-pass
For Example
I want to go to Nagano while i hold JR East Tohoku pass. What shall i do?
- Get off at Saku-daira and purchase individual ticket for Nagano
or
-Pay additional fare for Book a train to Nagano directly.

And ask about how additional fee is charged
- different price of each destination from the departure station
or
- as individual ticket from the last valid station

Sorry if my English isn't correctly

Details depend on the specific situation. Generally the options are:

1) buy the ticket for the remainder in advance (recommended)
2) buy the ticket for the remainder at the destination station's manned gate (not recommended because it potentially causes a delay at the manned ticket gates)
3) buy the ticket on board from the conductor (not always possible and not recommended)

For Example
I want to go to Nagano while i hold JR East Tohoku pass. What shall i do?
- Get off at Saku-daira and purchase individual ticket for Nagano
or
-Pay additional fare for Book a train to Nagano directly.

In this case, it is easiest to buy the ticket for the Sakudaira-Nagano section at a ticket counter before boarding the train. Note that it is probably not possible to use reserved seat in this case unless the train stops at Sakudaira. But it should be possible to use non-reserved seats even on trains that do not stop at Sakudaira.

And ask about how additional fee is charged
- different price of each destination from the departure station
or
- as individual ticket from the last valid station

As individual ticket from the last valid station (even if the train does not stop at the last valid station).

Thank a lot Uji san

Thank you @Uji. I have been looking at this issue myself as I hope to travel from Yonago to Osaka on the last day of a San-in Okayama Pass which is only good for part of the journey. I hadn't considered buying the ticket for the second part of the journey in Yonago.