Using a sensor on a light controlled by more than a single switch is often a problem.

The sensors are not generally available in more then single pole on/off configurations.

The [prp0bloem can be solved by running some extra wires, or using relays.

The chief problem is that the sensor has no way of detecting or altering the position of the switches and can only be used to bypass them without some additional controls (like a relay circuit).

Bypass is how they are often used anyway.
by placing the sensor in parallel with the regular on/off switch the light is turned on when dark outside, no matter the switch position.

Sensors will turn the light on with a predetermined off time. In parallel or wired as a "3-way" would do the same but with more than one location.

There are multi-location units, but they are not wired like a typical 3-way.

Post a make and model of the switch and link to the manual if you have it.

It is a Leviton "Single Pole and 3-Way Wide View Motion Activated Light Control." Cat. No. PR180.

I've added a link to the instruction manual on line below.

Thank you!

Here is a link that might be useful: Instructions

Define "shorts the circuit".

The switch you posted is intended to be used in 3-way configurations, the yellow wire is to sense the position of the switch on the other end.

So what's up?

That one WILL work fine, but only at one location.

I'll also ask, what is the problem? Is motion sensing mandatory at both locations?

I will try to explain a bit more. When I opened the wall plate to take out the original switch and install the motion-sensor switch, there were three wires: black, red and white. So I hooked these wires to the same colored wires on the new motion-sensor switch. The new switch also has a yellow/red wire but there was nothing to hook it up to. Should I have connected that to something and if so which wire? When I say "shorts the circuit" I mean that if I turn on the lights from the switch at the bottom of the stairs, everything goes dark and in the electrical box the switch is turned and I have to turn it off and on again. I am not an expert with this so I may be using the wrong terms. I appreciate any advice!

You don't just match the colours. You must determine which wire is the COMMON and connect that wire to the black wire of the switch. The yellow wire then connects to one of the travellers. The red connects to the load.
You will need to rewire the other switch as well. Make sure the power is connected to the common and not the load.
Connect the no used traveller from the motion to the common. Connect the yellow traveller to the other traveller connection on the switch. The 3rd wire coming back gets connected to the load.