Pokemon-go – I don’t understand stardust on Pokemon go

Like Samthere said, you can delay indefinitely, however id recommend keeping one Pokemon high to take gyms with. Don't power it up more than you have to but keep it high enough to get at least a few gyms. The extra star dust and coins you get should be worth the candies and stardust you spend to keep just one Pokemon high. I usually get rid of anything with a CP meter under 90%. It's probably good to set a goal like level 25, otherwise you probably will delay it indefinitely. Lastly, go ahead and evolve any Ratatas and Spearows (or other really common ones in your area) you can for the experience. Their evolved forms max out pretty low so they aren't really viable later, otherwise leveling will get really slow unless you are hatching eggs left and right.

The way to maximize stardust is to gain as many trainer levels as you possible can first, and then use it on pokemon that are close to maxing out anyway.

If you use it on a low level, it'll be a waste because in a couple of levels you're just going to find pokemon more powerful than the one you upgraded. So gaining as many levels as possible is your first priority.

That logic will always hold -- it is ALWAYS better to save your stardust until you're a higher level. But at some point you'll bite the bullet and decide you want to upgrade some pokemon now and do some battling. In that case, look at the half circle above the pokemon. This is an 'Upgrade Meter', where if it's filled all the way to the right, you can't use any more stardust. Pokemon you catch might start out with any amount of that already filled up. So use your stardust on a pokemon that's already mostly done for you.

See here for an example of the pokemon screen with the upgrade bar: http://imgur.com/r/pokemongo/mYu8Njh

In that case, the pokemon is about half-way powered up. I'd hold out for one that was already about three quarters upgraded.