Eggs spawned in a variety of ways - globally.

Some just appeared out of nowhere. These were the easy to get ones.
Some you had to cut bushes/grass to get.
Some you had to dig to get.
Some you had to kill baddies to get.

There were rare ones that only spawned occasionally, and some that were only attainable through the previously mentioned methods.

Then there was the trading. Oh yes, the trading.