1on1 - lets say you attack with 6 against 4. You now have 5 (one army must remain in source region) dice, oponent has 4. Now what happens is, each of you takes one die and you roll them, loser loses his dice and process is repeated until someone drops to 0. If you win, you take his region and you got as much army in there as many dice you had at the end of fight.
Hardcore - this is basically winner takes all, if you win, you keep all your dice and loser loses all of them (with exception on 1 that remains home)
Attrition - simmilar to hardcore, but you have chance to lose some army even if you win. I won't go into much detail, but it depends on how good did your and your oponent's dice rolls ended up
There are 2 start types, you either start with full map (each player have same number of regions, randomly ditributed) or with empty map and you are free to choose your starting point.
I will probably add more modes later on, so you have something to look forward to