Reddit mentions of Rode VC1 Mini-Jack/3.5mm Stereo Extension Cable, 10 Feet

Be sure the mic is set to +20, turn off auto audio on the camera, and turn the gain down for a normal level, usually about -20 dB. Also, be sure the you are using a SHIELDED cable between the mic and he camera, NOT just a headphone extension cable. They look the same, but a non-shielded cable will pick up a lot more hum.

If you have a camera (not sure about the T3i) that does not allow you to turn off automatic audio, you will need to put an attenuator (20-30 dB) at the camera end of the mic cable. This is not a great solution, but it can reduce the hum level.

It can be. I usually use an extension cord like this to get the microphone closer to the subject rather than mounting it on top of the camera. With an extension cord you can then mount the microphone just out of frame, close to the interviewees mouth. Either on a boom style mount above your talent or a simple light/mic stand just out of frame below your talent.

Thank you. Also the camera didn't come with anything to connect the mic into the camera, do I have to buy this?

I think a shotgun microphone should help here along with some blankets or acoustic treatment. You can pick up this shotgun microphone and some isolation to try and get that noise dampened. This will work if you are recording to a camera with a mic input, but if you don’t have a microphone input you can pick up this recorder which will also double as a recording interface. If you need to place your mic further away from your camera or recorder, this cord will give you some length to position it where you need. This is really nice if your camera is a few feet or more away from where you’ll be while shooting, as an added bonus the closer you place your microphone to your subject, the better it will pick sound and reject sounds you don’t want.

The shotgun mic should reject sound coming from the sides and pickup clear audio from the front. Place this close to your mouth and you’re good to go. I use a shotgun microphone to record voiceovers and videos at my desk because just like your place, it seems like my neighbors are always doing something loud. It’s useful to check your audio with some headphones to hear what background noise you might be picking up, then adjust.

If you’re still getting noise you’ll need to pick a time where you can record that you know to be more quiet. It’s a bit of a pain but unfortunately most home productions have to work around some sort of obstacle, just don’t let it keep you from making some videos!