What app is required to access and use my work computer from home computer

You would want to confirm with your office's IT people before moving forward with any method, because it depends heavily on your work network security configuration. Having said that, there are three simple options, listed in order of complexity to configure and expense to you or your company:

1. Back To My Mac - Basically, you sign into iCloud in the System Preferences tab on both your home and work Mac and then they should both appear in the Shared tab in your Finder whenever they are both online. You can then click on one and a button will appear in the upper right of the Finder window for Screen Sharing.

It's free, works seamlessly, and requires no configuration other than sign in and checking the boxes to use the feature on both computers. On the other hand, many business networks do not play nicely with the protocols and ports used for this connection method and therefore it may not work. There is nothing you can to fix it if your network is blocking the connection because there are no configurations.

For more information see: Set up and use Back to My Mac - Apple Support

2. A third-party VNC remote application - I like iTeleport for this as it's very simple to configure and doesn't get blocked by networks in most cases. With this type of program you want to look for the following feature; an app installed on both computers that makes the connection for you. Usually this is accomplished by having an account with the company that makes the app which allows your computers to use a middle-man to find each other, bypassing the security features of your work network that keep others from being able to locate your computer without knowing it's exact address.

This method is not free, but iTeleport for instance is like thirty dollars and thats it to use. It also has a significantly smaller chance of being blocked by your network, but still could be.

For more information see: http://www.iteleportmobile.com

3. A VPN connection to your work network plus the use of Remote Desktop Connection or Screen Sharing - This method requires expense and work to be done on your Business' behalf. Depending on the size of your company they may have this already available, but due to the expense and upkeep costs it is not something you could just ask them to put in place for you. Essentially, a VPN connection is a way to remotely access your office's closed network as if your computer were physically in the building without physically being in the building. It is a secure connection to the secure network. Your business would give you a small program to download that you would launch whenever you wanted to connect remotely, and you would then be able to use the built in Screen Sharing or Remote Desktop Connection apps on your Mac to connect to the other one.

For more information see "Share your screen" and "Share the screen of another Mac" here:OS X Mavericks: Screen sharing