There is no universal payment for finding a fossil. Whether you get anything at all depends on who owns the land, who owns the fossil, and what you do with it afterward.
On private land
If you have the landowner's permission to collect, the fossil is typically yours to keep or sell, subject to any agreement you made with the owner beforehand. Some landowners ask for a share of sale proceeds or first refusal on significant finds — settle this before you start digging, not after you find something good.
On public land
Rules vary widely by country and agency. Some public land allows casual collecting of common invertebrates for personal use but prohibits sale. Vertebrate fossils on public land are frequently the property of the state or federal government regardless of who finds them, and removing or selling them without a permit can be illegal. A permit system, where it exists, may require reporting finds to a museum or agency rather than paying the finder directly.
If you are working for someone else
Volunteers on an organized dig, or employees on a commercial or academic excavation, generally do not personally own what they find — the fossil belongs to the institution or company running the dig, per the agreement you signed on joining. This is normal and expected; the value to a volunteer is experience and access, not ownership. See how to volunteer on a fossil dig.
Museum finder's fees
Occasionally, a museum will pay a finder's fee or purchase a scientifically significant specimen from a private collector who found it legally, but this is a negotiated transaction after the fact, not an automatic payment for finding something.
The practical takeaway
Assume you are not owed anything for a find until you have confirmed land ownership, permission terms, and local law. Can you make money finding fossils covers the broader economics once ownership is settled in your favor.