The movement cost per hex is on the map page under the word Samurai, in the gray box. You can spend 1 action of the 5 to get 2 movement points. You can do this multiple times. Cross River -2 MP/Hex, Mountains -3 MP/Hex, Plains -1 MP/Hex.
You can spend Action points in any manner you wish from the 3 choices in the Actions section of the rules.
Actions (5 per turn per player)
Action Effect
Cost
1 Place 1 Chit of choice from your pool of chits.
1 +2 Movement Points
1 Initiate Combat Using 1 Chit.
Once all Action point are spent, then the next player takes their turn using the same method.
I hope this makes it more clear?