So what I don't get is how does the consensus mechanism for ripple work?
With bitcoin this is easy: If I want to state what transactions I consider valid I would simply mine on the according chain.
But how do I state which transactions I consider valid in Ripple?
You just run rippled.
CAUTION: Oversimplified explanation. -- At all times, rippled has an "open ledger" that is uses kind of like a scratchpad. When your server receives a transaction, it applies it to the open ledger. If the transaction applies successfully, your server relays the transaction to other servers. When the next consensus round starts, your server will propose (just to itself if it's not a validator, to the world if it's a validator) that the transactions in your open ledger be applied to form the next "real" ledger. The network reaches an agreement on that set of candidate transactions, applies it to the last closed ledger, and then builds a new open ledger based on that.