How can you know if my liberty 1799 coin is authentic?

You didn't say anything about the coin's denomination or design, so it's not possible to give a reasonable evaluation.

Loads of old-coin replicas are floating around, made as "collectibles" or as promotional items. These are usually identifiable in 2 ways - either they'll have the small Word COPY worked into the design (assuming they were made in the last 35 years) and/or you may see a seam along the edge where the casting mold came together (replicas are often cast in base metal rather than being struck).

If you can't find either indicator, my advice would be to have it looked at by a dealer or appraiser but be prepared to find out that it's not genuine.