You roll two dice, one representing you and one representing your enemy, for each battle, and report the results in the War/Battles thread.
Currently, you have to roll only for the Battle of New York, as we're not really sure who should roll for the UN... I suggest either the Secretary General(me), rotating responsibility amongst the active members(though Pacifistan, given it's neutrality, would be good here), or electing someone else. Earthling, after all, can only do so much.
Actually, since you were the first one to commit troops to defend Panama, you can roll for the UN there.

Remember to report your results in the Battles/Wars thread so I can tally them up, add the bonuses/penalties/etc. and the final result can be made.
Unless any other states have objections to this proposal, of course.
Furthermore, you will only be able to attack the USA once, and wait for them to have a chance to counterattack before you can attack again. This means you can only attack New York City, before letting them have a chance to strike back. You can, however, also attack the CSA in the same turn if you wish. The rule is you can attack as many countries as you want in a single "turn", but you are limited to one attack until the enemy has a chance to strike back.
Also remember that, as Israel is across the ocean, you will suffer a distance penalty, where the defenders automatically get +1 to their rolls. If you manage to gain land in the USA and attack from there, however, you will no longer have the distance penalty, by merit of already having a base there. Remember that if your offensive is turned back at some point, that the USA will gain a counterattack bonus should they decide to retaliate on their turn.
Hope that explained it.