You can use them both at the same time. Windows automatically extends or mirrors your desktop to work on both at the same time. Blue is usually VGA. Your card may come with a DVI to VGA adapter, and if not you can buy one for about $10.
Use HDMI cable to go from your computer to your TV because it carries and audio signal and connect VGA cable to your monitor. Blue is typically VGA but you can google VGA, DVI, HDMI and confirm. You can have them connected together at the same time like it was said in the earlier post you can either extend the screens or you can temporarily disable one or the other if you just want to use one without having to physically disconnect the cable.