Hello, I am new to arduino and electronics in general so please excuse any obvious shortcomings in knowledge. Anyways, I have a remote control switch for an outlet (see this product http://www.homedepot.com/p/Verdant-Electronics-Indoor-Outdoor-Wireless-Remote-Control-Kit-RC-017-3/202353566) and I want to be able to "push" the buttons with the arduino while maintaining the functionality of the button. I read elsewhere that all I need is a reed relay, but I dont understand exactly what that entails/ how do I set up that cirucit?
A relay is an electrically-controlled (and isolated) switch. Assuming you hear a "click" when the power-side of that gizmo switches on & off, that's a relay.
So for example, you can control a relay with the (low-power) Arduino to turn on & off AC power, and there is no electrical connection between the Arduino and the AC power (which keeps things safe for the Arduino and you).
Now to your situation - You'd need to open-up the remote-control unit and find the switch contact you wish to "activate". Then, you'd need to solder a pair of relay contacts in parallel with the switch. Now you can either push the button, or activate the relay and it will have the same effect.
It doesn't have to be a "reed relay". Just about any relay will do as long at it has a 5V coil rated for 40mA or less so it can be operated by the Arduino. The relay's contact rating is not important at all, since there is very little "power" inside that remote.
This means wires coming out of the remote to your Arduino. It also means that you have to disassemble the remote, risking damaging it, and that you'll have to figure-out how the switch is connected. If wires coming out of the remote connected to the Arduino is too "clunky", consider getting a 2nd remote for manual use.
What exactly is the Arduino going to do? Depending on what you are trying to accomplish, you may want to look into "home automation". [u]SmartHome.com[/u] is a good place to start looking into what's available. I have an X-10 system with [u]this programmable controller[/u]*. I've got several X-10 (and [u]Insteon[/u]) compatible light switches/dimmers and outlets. For example, the controller turns-on my front & back porch lights at sundown, then dims them a few hours later, then shuts them off at sunrise. I also have wired & wireless controllers that I can use to manually control this stuff, or of course, the controllable light switches can be operated manually.
I don't have it, but there are also interfaces that allow you to control this stuff over the net, or remotely with your smart phone.
There are a few other home automation protocols, but X-10 has been around for a long time... More than 20 years... The Home Depot gizmo might actually be X-10 compatible.
My system doesn't use an Arduino or any home-built electronics. But, there are ways to interface the Arduino with X-10 or some of the other home automation protocols, and that might be easier and "cleaner" than hacking the setup that you have.
- This controller uses an RS-232 connection, which your "modern" computer may not have. There is a USB version, but I don't see it on the website right now and last time I checked the software was still "beta". (The RS-232 software is kind-of "old" and it shows.) There are newer programmable controllers mad by other companies, but they can get expensive.
X-10 may not be the way to go as they have gone bankrupt 
X-10 may not be the way to go as they have gone bankrupt
True, their future is uncertain. But, one of their distributors has taken-over and the products are still being manufactured ([u]information here[/u]). And, there are lots of X-10 compatible products on the market. I believe it's an open standard. Most (all?) of the Insteon stuff SmartHome sells is also X-10 compatible.
It's kind-of strange that a new-better protocol (like maybe Wi-Fi) hasn't taken-over the home automation market, but it seems like none of the protocols dominate. I have a feeling, X10 is still the most common.
A couple of years ago I was looking for something "newer and better" because the software for my Insteon controller wouldn't run on Windows 7. There were no updates available, and no similar controller was being sold. The controller still worked, but I couldn't re-program it or re-set the clock. After looking-around to see what was available, what was popular, and the costs, I ended-up coming back to X10.
I'm really NOT a huge X-10 fan, and I'm NOT saying it's the best choice for everybody. The actual X10-manufactured products I've bought over the years have not been that reliable, and most of my flaky-failed X-10 dimmer-switches have been replaced with X-10 compatible Insteon switches. If Insteon still made a little stand-alone programmable plug-in controller like they used to, I'd go with a fully-Insteon setup.