using arduino to open and close a circuit

I'm trying to get basically pass a wire through 1 input of the arduino and out another and have the arduino open and close that connection. Its the equivalent simulating a momentary switch on a doorbell to ring at a preset interval (every 10 seconds, for example). I'm fairly new to programming, and having a hard time finding what I'm looking for and would appreciate any help I could get.

Try some of the examples in the Learning section. Reading an input, writing an output are very basic functions.

You should use 5V relay that draws less than 40mA. Or if relay draws more current, you should use a transistor to switch the relay from Arduino output.

I have a basic idea how to assign pins, and have done a lot of the learning with the LEDs and such, but didn't know if what i am trying to accomplish is even possible or not. I wasn't sure if the arduino is capable of connecting two pins (1 input and 1 output) and just pass the connection along. I've tried looking through the tutorials and learning sections, but I learn better from working backwards from something that works and figuring out why, than trying to figure out what I need to do to make it work. Its very counter intuitive with this type of thing lol.

I wasn't sure if the arduino is capable of connecting two pins (1 input and 1 output) and just pass the connection along.

Can you describe what it is you are trying to do? The solution could be as simple as digitalWrite (outputPin, digital read (input pin)); inside a tight loop.

aspyr2: I have a basic idea how to assign pins, and have done a lot of the learning with the LEDs and such, but didn't know if what i am trying to accomplish is even possible or not. I wasn't sure if the arduino is capable of connecting two pins (1 input and 1 output) and just pass the connection along.

Only if the signal on the wire is a +5vdc logic level on or off voltage can you directly wire it to a arduino digital input pin and then in your sketch software you read the value and send it to a arduino output pin to where you need the signal to go to, but only if where it is going doesn't require more then 40ma of current or less. Even then you would also require a separate ground reference wire wired to the arduino ground pin for that to work. So pretty limited and you didn't give any technical information about what the electrical values on the wire coming to and from, such as voltage range, current flow amount etc. So when you were told you could use a relay it is because the output part of a relay is just a set of contacts that are open or closed depending on if you activate the relay's coil or not via an arduino output pin. Such a set of 'dry contacts' can be pretty good at just passing through or not whatever is going through that external wire, up to of course the voltage and current limits of the relay being used. So the answer to your fundamental question "can you...." is it depends on what electrical properties are on the circuit you wish to 'pass through'. And the method and components you will require to it also depends on the same answers.

I've tried looking through the tutorials and learning sections, but I learn better from working backwards from something that works and figuring out why, than trying to figure out what I need to do to make it work. Its very counter intuitive with this type of thing lol.

The application is for a nursing home door alarm. There is a keypad on the inside to get out and a doorbell to get in - each one temporarily bypasses the alarm for about 10 seconds. It has to have a momentary connection each time to activate the bypass.

I’m basically looking for a way to unhook the doorbell and have the arudino simulate a momentary connection between the two wires coming from the device, break the connection with a 10 second delay, then loop. I couldn’t figure out how to get it to bridge that connection.

aspyr2: The application is for a nursing home door alarm. There is a keypad on the inside to get out and a doorbell to get in - each one temporarily bypasses the alarm for about 10 seconds. It has to have a momentary connection each time to activate the bypass.

I'm basically looking for a way to unhook the doorbell and have the arudino simulate a momentary connection between the two wires coming from the device, break the connection with a 10 second delay, then loop. I couldn't figure out how to get it to bridge that connection.

As has already been stated a few times, you'll need either a transistor, relay, or combo, depending on the voltage/current requirements.