OK - got Fishy to join so this should be fun. I realize I have to give a basic Risk instruction.
1) You win the game by taking all the territories on the board. ie. You have to kill everyone else.
2) You are given bonus armies at the start of each turn for owning territories (I believe one bonus army per 3 owned with a minimum of three every turn. If you have one territory, you get three. If you have 6, you get 3, if you have 9, you get 3, if you have 11, you get 3, if you have 12, you get 4, if you have 15, you get 5 and so on.)
3) You get extra bonus armies at the start of each turn if you own an entire continent. Different continents have different values because some are easy and some are hard. Australia gives you 1 extra, Asia gives you 4 extra armies. It's really hard to own Asia and relatively easy to hold Australia or South America.
4) You will get a card at the end of each turn if you have taken at least one territory. If you take none, you get none. If you take, 1, 3, 7, 10 or more, you get one card. It's generally important to take one territory to get a card each turn, although in this game, it won't hurt much if you don't.
5) Cards have 4 things on them - Circle, Diamond, Star or Wild. C,D,S cards have a territory associated with them. Wilds do not. When you have three of a set or three different, you can trade those in at the start of a turn. 3 Circles gets you 4 bonus armies, 3 Diamonds gets you 6, 3 Stars gets you 8 and 1 of each gets you 10. A wild can be used for any card, but if you are lucky enough to get 3 wilds, you can trade them for 20. If you own the territory associated with the card, you get 2 extra bonus armies on that territory. You can have up to 5 cards before you have to trade them at the start of your turn.
6) If you take the last territory owned by a player, you get his cards. This can be pretty important.
7) You can only attack bordering territories. Some borders go across oceans (ie, North Africa to Brazil).
The card thing sounds complicated, but it isn't - you'll get it in when you get your second card.
Ok - the dice: If you are attacking and have three or more armies, you throw three dice. If the place you are attacking has 2 or more armies, they throw two dice. The best (highest) die or each player is compared and the loser loses an army - if they are tied, the attacker loses) Then the second best die are compared and the lower loses an army (again a tie goes to the defender). If the attacker has 2 armies, he throws 2 dice. If the defender has 1 army, he throws one die. All the above rules stay the same.
If you attack with 8 armies against 5, you throw three and the defender throws 2. Two armies will be lost and you can go again. If you attack with 8 armies vs 1 army, you throw 3 and he throws 1. If you attack with 2 vs 5, you throw 2 and he throws 2. If you attack with 2 vs 1, you throw 2 and he throws 1. This again sounds a little complicated but is obvious by your 2nd turn. Bottom line, it's best to attack and it's best to have a lot of armies.
This sounds complicated too but becomes easy. Examples:
Attacker 6, 4, 1 Defender 6, 3 - each loses one (6v6 goes to defender, 4vs 3 goes to attacker)
Attacker 6,5,1 Defender 5,4 - defender loses 2 (6v5 goes to attacker, 5v4 goes to attacker)
Attacker 5,4,4 Defender 5,5 - attacker loses 2 (5v5 goes to defender, 4v5 goes to defender)
Again - sounds complicated but it's not. The game takes care of it for you. The bottom line, attack with a lot. Put a lot to defend when you can.
In this game to start, you might have to attack 3v3 sometimes (that would be three dice for attacker and 2 for defender) and it's a crap shoot. However 30 v 30 is pretty big favorite for the attacker because of the extra dice.
These are the basics - you'll catch on really quickly. It's not as complex as it sounds.
Basic idea - attack with more than are defending and take territory and defend continents. That's about it. Oh yeah - kill everyone else.