In FF8, how do you defeat Diablos when you first get him?

As I recall, Diablos is pretty challenging when you first get him if you haven't been doing any grinding or excessive magic-drawing early on.

The key to the fight is the spells that you can draw from him. He always carries Demi, and will have either Cure, Cura or Curaga depending on his (i.e. your) level. Draw these and use them to your advantage.

The Demi spell instantly removes 25% of the target's current HP. This means you want to draw it and cast it as your first couple moves. The more HP he has, the harder it hits. In this way, you can drop him to half health in two shots.

From there, beat him down with standard attacks and magic. As a flying monster, he is weak to Wind. Make liberal use of the Cure-family spells you can draw from him.

His Gravija spell hits extremely hard, but it works the same as Demi, it just takes a much higher percentage of your health. If he puts you into position for a Limit Break, you can also do a lot of damage that way. (Remember, you can hit the Circle button to retry for a Limit Break if you're at low HP).

Finally, don't be afraid to use any healing items you have. Items are plentiful in FFVIII, and you'll be able to easily resupply later on.

The key for me was having blind (drawn from the Granaldo Boss not long before you are first able to battle Diablo). If you draw a full stock of it for at least one character, and have it equipped to ST-ATK, between attacking with that character and casting it you should be able to affect him fairly quickly (note that he has a high resistance to blind, but is not fully immune).

Once you successfully hit him with it, it is almost impossible for him to kill you - he will cast Demi and Gravija most of the time, which can only reduce your HP to 1, not kill you. Only his punch attack can kill you, and he will almost never hit with it once blinded. You can leave your characters on low health (using their limit breaks with abandon) and just Phoenix Down them if they do happen to be hit by a lucky punch. As per the other answers here, still start by spamming Demi, as that will do far more than even your limit breaks (if you are attempting this fight early-game) until his health is reduced to a more manageable level.

I seem to recall him having a not-so-fun melee attack as well. Blinding him was always the first thing I did, though it takes a few attempts to do so.