Cassie, Laz's offer to show you how transmutes work is very generous, and I highly encourage you to take him up on it. He routinely works in the transmute room at cons--he's an expert. I agree that sitting with someone as they show you how it works on real tokens will probably be a lot more clear than just reading about it.
If you have any specific questions about transmutes, feel free to ask them. For what it's worth, here's a couple of tips I wish I knew earlier than I did:
1. Rare, Uncommon, and Common tokens turn into trade goods. Ten Monster Bits turn into 1 Golden Fleece. Gold can be transmuted into 1k, 5k, or 25k bars.
2. One type of trade goods takes 25 of a particular type of token to make a trade good. (Aragonite, Dwarven Steel, Elven Bismuth, Minotaur Hide, Oil of Enchantment.) For example, you need 25 rare weapons or armor to make 1 Aragonite.
3. The other type of trade goods take 25 units of the appropriate tokens to make a trade good. (Alchemist's Ink, Alchemist's Parchment, Darkwood Plank, Enchanter's Munition, Mystic Silk, Philosopher's Stone.) A rare is 6 units, uncommon is 3 units, and common is 1 unit. So, you could make a Darkwood Plank by turning in 8 uncommon tokens plus 1 common token that turn into DP, or any other combination that adds up to 25. (I did that a lot when I was starting out. As you gather more tokens, you could wait until you have 25 uncommon tokens that turn into DP, and just turn that in for 3 DPs. You can also turn in 25 rare tokens that turn into DP in order to get 6 DP.)
4. Tokens printed in 2018 or later (mostly) have a two-letter code at the top. It tells you what the token transmutes into. For example, "AG" is Aragonite and "PS" is Philosopher's Stone. For older tokens, you can always check the token database for the "Exchange Program Classification" line to confirm.