Hi Jared,
Connect/turn on the external monitor. Open System Preferences on your MBP > Displays. There should be two windows, one for the external monitor and one for the MBP. Click on the window for the external monitor. Click on the Arrangement tab. Uncheck the box for Mirror Displays. This willallow you to set each display to its own resolution. On the external display, click on the pref window for the external monitor display setting. Click on Display. Set the resolution to what you want. On the MBP's display, click on the pref window for the MBP's display and set the resolution to whatever you want. You'll be in what's called "extended desktop mode." You'll have to move the "pointer" all the way to the edge of one display to get it to go onto the other display. Open whatever you want, and drag it to the extended monitor. Set it to full screen. Open another whatever on the MBP's display and set it to full screen. You should be full screen on both displays.