Even if you wired it backwards, which you didn't, it would not cause the breaker to trip. Something else must be wrong.

could be several things.

first, check resistance from the silver to the brass terminal.

then check each of them to the ground term and then each terminal to the casing

with the terminal description you gave, there really isn't any way you could hook it up wrong.

Now if things work out with the ohm meter, you may simply try a larger breaker. NEC lists a 1/4 hp motor at 5.8 amps. The inrush current can easily be 4 or 5 times (or even more) that. You can put a motor on a breaker up to 250% of nameplate rating to accomodate the inrush current.

drop backwith the meter readings first though.

Thanks for the response. The ground screw is actually screwed into the case so the ground terminal and case are the same.

After getting my reading glasses and a flashlight I noticed that the top terminal (brass screw) is labeled "1" and the bottom terminal is labeled "4". I have my hot lead attached to term 1, neutral lead to term 4 and bare conductor to the ground screw (case).

With no wires attached, when checking the resistance between term 1 and 4 it is a direct short (no resistance) thus the problem. It is open (no continuity) between term 1 and ground and between term 4 and ground. I still do not know how to wire it.

It sounds like you have a direct short in the motor. In the olden days, you'd probably have the motor rebuilt. In 2007, it's probably time to buy a new fan motor. This isn't a supply wire problem.

I went back and rechecked the resistance between term 1 and term 4. It is actually 4.5, not zero. I have two of these fans. The second one I had not wired yet; however, it has the same reistance measurements as the one I'm now trying to wire up.

Are these new fans or used?
There is a capacitors used for starting, and possibly a run capacitor as well. Even if there are two capacitors they may be in the same 'can'.
Look for a bump on the side of the motor.
Motors usually sit and hum for a few seconds if the capacitors are bad, so if you have someone else turn it on while you are standing right beside it.

Both fans are new. They do have the "bump" on the side. I installed a switch close to the fan. The breaker tripped instantly when I flipped the switch. No humming first.

Does the other fan work?

If they're new, you should have installation instructions. Or are these cheapo Chinese sweatshop motors with no papers?

"Or are these cheapo Chinese sweatshop motors with no papers?"

Isn't everything these days from China?

Sounds an awful lot like a dead short.
You can try to troubleshoot them, or return them.
They could have a pinched wire between the cap and the centrifugal switch, or even in the winding connections.
The DC resistance of the windings is usually very low. The AC impedance will be higher.