How would you "study" Risk?
This is purely off the top of my head, but the following come to mind:


Learn the most likely die rolls
Look at paths of contact (eg, you can only get to Australia through Siam)
Find "choke points" (building off the contact paths)
Note that Continent bonuses are in proportion to not only size, but difficulty in holding/winning them
Gameplay can be wildly different with two players instead of 3, 4, 5, or 6

ultimately all games devolve into 2 player games, but knowing how to handle the higher number of players is key to surviving long enough to be in the final pairing

The Neutral player in a 2 player game can have some interesting consequences when playing strictly

because they are not required to be eliminated to win, you might only attack to gain a Risk card
depending on how the cards were dealt, they can be used to your (or the other player's) advantage as a buffer to weaken attacks (or strengthen defense), forcing the attacker to expend more armies to defeat the defender



Everything else I can think of come with time and practice:


like when to attack / when not to attack

for example, if your contact territories are heavily defended, but your non-contact territories only have one or two armies, it may be a Bad Idea&trade; to attack from there if the enemy territories are moderately-well defended (ie, they could attack back form multiple directions easily against a weakened contact territory and wipe-out the middle of your holdings)

when to hold cards / when to turn them in

for example, if you know that your opponent must turn his cards in on his next turn (he has 5, and therefore has a set), but you have the option (perhaps you have a set, but you have four cards, and can therefore wait a turn), it may be worthwhile holding yours till after he turns his in to get the next-higher army value from them
in my experience, holding your trades only notably impacts the game early on (before the turn-in exceeds 10 armies)

etc


And don't forget the psychology of the game, too:


Some players "want" Africa and will do [almost] anything to get/keep it (for example)
Aggressive vs non-aggressive play styles
etc