Well, it's explained in the later novels (characters basically do recaps on previous Seldon Crisis situations, as well as their solutions), so I don't want to spoil it too much for you. In each case, as per Seldon's design, the answer is almost inevitable.
I haven't read them in a few years, but as I recall, the first few crisis points:
(Headers to remind you without showing the spoiler, if that's enough -- don't want to ruin the fun, if you re-read :) )
Balance Of Power
Basically, they didn't try to fight them, but they made sure the enemies of the Anacreonians knew what was happening; their enemies couldn't risk one group having access to nuclear power, so a stalemate forced them all to leave the Foundation alone. I believe this is the 'obvious' one you reference.
Next they instituted a 'Religion' behind technology and used that to make fighting the foundation a 'Sin' with demonstrable results; the trained techs on other planets didn't really understand things, just know how to use them. The foundation retained the ability to put them under Interdict, at which point all of their foundation technology ceased working.
The third one was simple; dependence via commerce. The Religious angle had played itself mostly out, as worlds were aware of it. But Hober Mallow stuck to the idea of trade alone protecting them. They provided a product that couldn't be had anywhere else, was better than what was available elsewhere, and forced the enemies into dependence on their product. A little 'planned obsolescence' and they had enemies that couldn't afford to make war against the Foundation, as they needed Foundation supplied tools to do so with.
Oh, I should mention -- these are the EXTERNAL crisis points. There were internal ones, too, at each Seldon Crisis, but I don't think you were asking about them.