Q:

How were the first children of Gaia conceived?

According to Greek Mythology, Gaia had many children. All of them were with a partner, except for three:

Uranus
Pontus
Ourea

Is it ever explained how these children were conceived?

A:

Ourea I'd never heard of before, so I looked that one up. Turns out that was not one entity, but rather a word used to designate the mountains. Wikipedia names 10 of them, but other references I found seem to indicate any mountain was considered one of the Ourea. So this is effectively saying "the Earth gave birth to the mountains".
That same Wikipedia reference claims they were the "parthenogenetic offspring of Gaia alone", which means there was no partner; they just happened.
I'm not sure if there's another original source that mentions them, but this is what Hesiod had to say:

And Gaia (Earth) first bore starry Ouranos (Heaven), equal to herself,
  to cover her on every side, and to be an ever-sure abiding-place for
  the blessed gods. And she brought forth long Ourea (Mountains),
  graceful haunts of the goddess Nymphai who dwell amongst the glens of
  the hills. She bore also the fruitless deep with his raging swell,
  Pontos (Sea), without sweet union of love.

That last phrase there is key. It appears to be applied to Pontos only, but since no partner is mentioned for the previous children either, I think we can assume it applies to them as well.

