There are two threads on this site that may really help you out
Lots of kind members have adoption centers and things on
this thread, where you can have a look round and, if you follow the rules of the particular threads, adopt some free pets. How cool is that!? Make sure you only adopt from people who say in their post you can, though, and be sure to follow the rules! This forum is great for new members, and it helped me get some good pets into my collection to start off with.
However, if you want to trade for pets, you should check out
this thread, where members post pets they're looking for and, if you have them, you could trade! Or maybe you could post yourself advertising what pets you would like to trade for? Remember, though, asking for pets for free is against the rules.
If you have any other questions, feel free to send me a PM, I don't bite! I'll try and help as best I can!