I noticed that the blower fan was running but AC was not cooling.

I checked circuit breaker and it was open.

When I reset the circuit breaker, the compressor fan ran for a few seconds and then shuts down again. The circuit breaker was tripped again.

I would appreciate any help

Weak or Bad Breaker, or overload caused by Compressor, or Compressor Fan.
Ampprobe will determine quickly. Or disconnect 1 or the other for test.

I replaced the cicruit breaker. However, it does the same thing. How do I check the amps ?

Amprobe is an Amp Meter that will show amount of current being drawn.
Your Outside unit has 2 likely culprits(compressor or fan)Clamp around each individually
To determine shorted or defective item. With no meter, you could disconnect one and see if it trips, if it doesn't trip, you probably disconnected bad item. Replace
Electricity can kill, Be careful
Capacitors can short also. Compressor and fan both have capacitors.

OK. Thanks. I checked the fan and compressor. The compressor trips the circuit breaker. I checked the capacitor with a meter and it looks OK.

You also need to check that compressor or capacitor not shorted to ground(at compressor)
Hopefully AC guy will be able to help with further test, or replacement suggestions.
Good Luck.