How are travel expenses paid by conferences? Is there a standard way they are paid?

We'll concern ourselves only with cases where it's stated that the conference will pay travel (up to a specific amount). However, does the speaker pay and then get compensated for receipts? Does the conference pay the tickets? Does it pay them in advance?...

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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.