How are travel expenses paid by conferences?
In my experience, most times the person being compensated pays for their travel in advance, and then the conference recompenses them (save your receipts!).  

Occasionally, however, the conference will arrange (and pay for) the dominant expenses (typically airfare and/or lodging).

The first is often actually preferable for speakers who can afford delayed recompense and trust the organization, since it gives more flexibility in making one's plans.  Usually, however, you don't get a choice.