How do I check the clutch fluid to a 1999 Mercury Cougar 4cyl

There is not one. You can check level visually by removing top of of fluid reservoir.

Fat as possible.

If the fluid was low the clutch pedal would go to the floor and stay there, so that is not the problem. You most likely have a worn out clutch, completely worn out. The clutch fluid reservoir is under the hood on the firewall next to the power brake vacuum booster.

Most hydraulic clutch systems have a small reservoir near the brake master cylinder that uses DOT3 or DOT4 brake fluid. Some systems,however, use the brake master cylinder for the clutch fluid supply.

down side of master cylinder.

You need to check and see if the reservoir is full of fluid. If its low, it may have cavitated and drawn air into the system. If its low it is leaking out of the master or slave cylinders,the seals are going bad in either the master cylinder on the fire wall or the slave cylinder at the bellhousing.
First thing to check is the reservoir level.

either you have air in the hydraulic lines or there is a problem with the final linkage. Is the slave leaking? Have you had to add fluid to the reservoir? Was the reservoir ever found empty? If yes, fix leak and bleed system. If no, problem is probably in the fianl linkage after the slave. Slave my be loose or linkage worn out? Let us know what you find and if you need more help.

On the firewall mounted on the brake booster,the booster is round,,almost like a puffed up pancake,

what do i have to do to change the clutch in a 2000 mercury cougar 2.0 thanks

V6 ? 4CYL? Have you verified SPARK? Did anyone check the "fuel pump inertia switch?" Its in the right front kick panel. If it was a "Anti-theft Issue" the light would be on or flashing.