[thejeff]

"How not to die" is probably more advanced than needed.

Dominions is a very variable game. We really need more data to know how to help.
What nations have you tried? How far do you usually get before you start getting overwhelmed? What turn? How many provinces?
Standard expansion against the default independent level of 5 is taking 1 province a turn starting on turn 2, reinforcing that starting army and sending out more expansion parties every other turn or so. 10-15 provinces by the end of the first year (unless you're running into other nations) and picking up speed.

Against the AI, some PD is actually useful. It doesn't help much in actual battles, but the AI bases its decision on whether or not to attack you in part on whether it thinks it can take your border provinces and PD plays a role in that.

Agreed that Akashic usually isn't worth it, use the individual searching spells. But if you haven't figured out the magic system enough to make use of those gems yet, it doesn't really matter.

Dominions is a game of counters and counter-counters. The AI is widely considered to be terrible, despite thrashing most of us when we started playing, because it doesn't know how to counter tactics used against it. Its favorite technique is the huge armies you've run into. The counter to that is not to fight a war of attrition against it, but to fight it with things that huge armies can't really hurt. SuperCombatants and/or Elite sacred troops, mostly. Trickier is artillery mages behind a shieldwall.
Try a nation with strong sacreds, give them an appropriate bless and watch how they cut through huge armies.
Try playing with an awake SC pretender. There are better ones, but try a Dom10 Wyrm with no magic. That's about the simplest to use. Put him in the back of the field with orders to Hold, Hold, attack. If he dies, call him back.

More generally, bump up the independent difficulty. That'll slow your start down, but it'll slow the AI down more, since it's not good about picking which provinces it can take.
I did better using maps with more provinces/player so I had more room to expand before getting ganged up on by the AI.