X-COM - First Alien Invasion

Hint 1:
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Be wary of the power-up question marks. Yes, they can be 
neat, but they often hide a land mine that can take out a 
trooper or an alien in one burst. 

Hint 2:
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Rockets and blaster bolts affect not only what they hit, but 
also everything in adjacent squares. So although a rocket 
launcher's range is six tiles, it can damage seven tiles 
(six tiles plus a one-tile fragmentation range). 

Hint 3:
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Use the Move and Fire order to duck out of a door, snap off a 
shot, and then duck back inside. This hides your soldier from 
return fire during your opponent's turn. 

Hint 4:
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Use the Etherals' psionic power on the most powerful enemy 
target visible. Although the attack does little damage, the 
psionically controlled target may fire at its fellow troopers 
(or at itself for that matter). You want that friendly fire 
to hurt.

Extra damage
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Missiles and blasters can damage objects in squares that are directly 
next to the target due to fragmentation damage. This effectively extends 
their range by one square.