While the term of imprisonment and amount of the fines may vary from case to case - here is the basic info the OP asked for:

Criminal Penalties: While in a foreign country, a U.S. citizen is subject to that country's laws and regulations, which sometimes differ significantly from those in the United States and may not afford the protections available to the individual under U.S. law. Penalties for breaking the law can be more severe than in the United States for similar offenses. Persons violating Qatari laws, even unknowingly, may be expelled, arrested, or imprisoned. Penalties for possession, use, or trafficking in illegal drugs in Qatar are strict, and convicted offenders can expect jail sentences and heavy fines. Penalties for drunk driving and other alcohol-related offenses are treated with severity in Qatar and may result in heavy fines, imprisonment, or expulsion from the country.

Qatari jails are not like US jails - you are housed with several others (who may have committed more serious/violent crimes), you will not have access to legal counsel unless the authorities permit it (which they do, but it is severely restricted in some cases), you will probably not be allowed visitors.

When your sentence is complete, you will be deported. (At your own expense - if you cannot afford the price of the airfare home, you stay in jail).

Hope that helps
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