Welcome!
Magistream has extensive worldbuilding which I myself only recently started getting into despite being on this website for ages, it's actually right up my alley so it's a shame that I didn't start reading earlier! That being said, the game is completely playable if you are not really a reader type.
There are many ways to acquire creatures: you can pick up eggs from the stream (tip: there are more streams than the one on the front page and different kinds of eggs can be found in each of them, you can find them by clicking "world" and any of the locations that have (tributary) after the name). Besides the stream you can visit a shop to buy eggs and items, at the moment earning gold is tougher than it used to so the prices are rather high, but the issue is being worked on. A couple of ways to help with that at the moment are attuning to an element (a quest) and buying the alicanto heart from the artificer shop (you must first complete a quest to gain access to it). You can also acquire unique eggs through quests, but be aware that most quests you can only do once! You can find in the Mercado section free quest help if you need it. You can also buy creatures from other users, or find them in giveaways posted in the Zocalo section.
As for growing creatures, I use the three methods that aflame mentioned, and my creatures grow up from egg to adult typically in justs a couple of days.
If you have any questions, feel free to ask! I hope I didn't just make your head spin with all of that info, I promise it's not as complicated
I hope you will enjoy your time here!
![Waving :wave:](./images/smilies/Byebye.gif)