2-player games are simple. Attack.
The goal of risk is to eliminate all your opponent's armies. Armies are both offensive and defensive assets. SImply put, the more armies you get and the fewer your opponent gets, the more likely you are to win the game.
In 3+ player games there is not a direct relationship between your attacking potential and being attacked. If you attack A, A is worse-positioned to attack you, but that is not true of B, C, etc. In 2-player games, the more you attack and the fewer reinforcements your opponent gets, the more likely you are to gain and increase your advantage.
There can be some exceptions. The most common is if your opponent is unlikely to have a set of cards, there are limited points of contact, and you can "throttle" him by placing enough armies on those contact points to deny him a territory and hence a card. Another is to not expose his forces. Consider an extreme case where he has 200 armies on Victoria, and also holds the rest of Australia. You should attack Indonesia (Signapore) but NOT the other connecting countries. Make him unable to use his huge force next turn.
Generally though you should attack all-out to deny your opponent reinforcements.
In mature games where the card value is high, the game will often ebb and flow. You should usually exchange at the first opportunity, because the territories you conquer will mean more reinforcements for you and fewer for your opponent. The exception is if you have an advantage in the game and know you can survive an attack. If you are gaining a little each turn, better to wait rather than cash for some number and have him cash in turn for that number plus five. But sometimes there is nothing you can do but hope for a set and hope you can survive if he has a set.
There are other strategies in games where 2 active players remain but others have dropped out. In these it's important to attack only your opponent and not zombie territories. You want your attacks to not only gain for you but to deplete your opponent. Sometimes you can do it if you (a) need only one territory to take a continent and (b) can hold the continent.