When and Where?
Basically if in a month travel, you can purchase it
at ticket vending machine and ticket office(noted open hours) both,
while in Osaka, Kyoto and any region's major JR stns
and even "KIX(airport)" or "JR Osaka" stn which has no Shinkansen tracks/rail.
But basically ticket office staff work is very faster
than vending machine(English button exist) touch screen like this
https://youtu.be/DCrM4nIs9nsexcept busy time zone or someone(elder or foreigner) stucked.
But if you using "Japan Rail Pass" or other similar tourist pass,
you can not order(not purchace) at ticket machine.
(bc must show the Pass when ordering)
And, NOT Shinkan(z)en, "Shinkan(s)en" is.
Also Shinkansen ticket is not a "card" type, paper ticket like this.
http://i0.wp.com/www.chooseyourlifeadventure.com/wp-content/uploads/20...(Insert ticket gate and don't forget receive when dep stn ticket gate)
https://youtu.be/sDn1Ggo5P-0 (This is Rail museum's special skeleton covered one for understanding machine inside)
(note) If use mentioned above pass, you can not use automatic ticket gate.
Shinkansen "reserved seat ticket" sales start date is just one month before fr travel date.
So if long stay travel over a month, you cannot.
(That section's Shinkansen ticket is no sale for out of Japan as online booking)