The basic rule for good play in Axis & Allies is Don't fight a battle you're not going to win. If your foe is stronger, retreat. Don't attack if you are going to destroyed with a counterattack.
Spoiling Attacks can be an important tactic. Attack and then withdraw before destroying the opposing force, which could leave you vulnerable to an enemy counterattack.
It can be worthwhile to risk a counterattack if you are taking an enemy factory, and is usually worthwhile to take an enemy capital.
On the defense, focus on building a strong force to defend your capital. Launch attacks to clear the adjacent areas, but minimize exposure to counterattacks. Aircraft can be useful for this, so don't forget to remove your AA Guns from those areas.
Don't neglect a front entirely. Even 1 infantry per turn can prevent your foes from consolidating control.
Don't build a factory where it can't be defended.
In A&A, the number of units is more important than its strength. You should be building at least half your units as infantry each turn, even on the attack (unless your foe is already weak). However, an all infantry force is a poor attacker, so try to build a little armor or artillery, even on defense.
When fighting along a front, keep your forces concentrated. If your foe is splits his force, attack the split force.
Don't let your foes take areas for nothing. 1 infantry unit prevents a blitz and will divert a number of opposing units.
As you want to keep forces concentrated, but not leave areas defenseless, your typical position on a contested front will be a large force, with small forces adjacent.
Keep track of your opponents' threats, and try to create multiple threats of your own.