Re: Aren't transactions rather slow?
When a client makes a transaction it is broadcast onto the network and takes just a few seconds to reach most of the network. At this point the transaction is not confirmed but the payment processor the vendor is integrated with will check for other unconfirmed transactions on the network that would indicate a double spend.
The vendor can decide whether this is sufficient security and for low value transactions like taxi fares and restaurant tabs it probably is.
For larger value transactions one confirmation is targeted to take approximately ten minutes, it can vary significantly though sometimes it can be much longer. The vendor decides how many confirmations are required before considering the transaction irreversible and thus accepted.