Warp your ship in front of the oncoming Alien AVIANs by simply touching the screen in front of the AVIAN attack wave. This'll destroy the oncoming marauders as they collide with your ship.
When power ups appear, simply pluck them out of orbit by touching the icon on screen. Some of the power ups are storable, so you can use them later - these will appear at the bottom of the screen, whereas others are used immediately.
Storable power ups: once you've got these, simply poke the power up icon at the bottom of the screen to use them, and you're good to go.
The MX-409 bigGun - this weapon appears intemittently in orbit. To use it simply aim by poking at the screen where you want it to fire - each press of the screen fires off a few plasma bullets, so hit the screen rapidly if you want alot of damage to happen.
Alien AVIANs that make it past you will collide with the Earth, damaging it. Your Earth health is at the top of the screen, and if it goes to 0, the Earth is evacuated of all essential personnel, and the game is over.
For each attack wave, you can also see the progress of the attack by the health of the AVIANs as well using the bar at the top of the screen - when it goes to 0, the wave is done.