The whole flow is two calls: quote to get a pathId, then assemble to get a signable transaction. A pathId lives ~60 seconds. The examples below swap USDC for EURC. Any pair listed by GET /info/tokens/101 works the same way — swap the mints and nothing else changes.
1

Request a quote

The response carries outAmounts, an astrolabe.tier (which size tier priced it), and a pathId.
2

Assemble the transaction

transaction.data is a base64 VersionedTransaction.
3

Sign and submit

Decode transaction.data, sign as userAddr, and send it through any Solana RPC (Astrolabe uses FluxRPC, but any works). Astrolabe holds no keys.

JavaScript

userAddr in assemble must match the one from quote. A mismatched or expired pathId returns 404.