How does my nation build military strength and defend against hostile takeovers?
Invasions, trade, negotitations, basically everything is RPed in the forums. Its up to you to decide how big your military should be and what sort of equipment it can have. You can say "I have a military of forty billion people!!!" if you want, but this is generally looked upon as n00bish and stupid. The NS Military Rule of Thumb is that total combat troops in wartime should never exceed 5% of your population (some people go as far as 7%, but these are generally conscript (read: sucky) armies. As for arming your troops, you can either give them basic weapons yourself ("y grunts are armed with AK-78s"). Also, some people have "storefronts", where you can RP buying something, like a Nimitz carrier, that you normally couldn't produce on your own.
For an example:
Thread: Invasion of Kerblakistan
Former Marsupiul Union: The FMU has decided to reassert its claim over Kerblakistan. We are deploying 5000 troops the region. This include 25 T-80 tanks, and 3000 foot troops armed with AK-47s.
Kerblakistan: We have mobolied the Kerblaky Defense Force of 1500 men, they are moving to counter....these are entirely infantry and are armed with surplus Ak- Negative 12s.
Ok thats a really bad example. For better (and more coherent) examples, read the stickies in the NationStates and International Incidents forums.