You need to connect both monitors to a computer. Monitors do not daisy-chain (in general). The exception are some SCART-enabled monitors.
What is your source (desktop)? What is the make/model of your new monitor? Please add a comment with the video outputs/inputs for your source and second monitor.
Many newer desktops have two or three outputs. (Some video cards have display port outputs which with active adapters can support 2 monitors each.)
If your computer has two or more outputs and your new monitor has an input compatible with the extra output, get the appropriate DVI, DVI-HDMI or HDMI cable for your new monitor. See the next section if both monitors have VGA input.
If you have a desktop with only one video output, you may be able add a video card to support two monitors. (Depending on your computer, you may need to upgrade the power supply to support a video card.) Then get the appropriate adapter or cables to add the second monitor. (Note: if both of your monitors have only VGA inputs, check the specs for video cards carefully. Not all modern cards support analog outputs on their DVI, HDMI or Display Port connections. These digital outputs would require a digital to analog converter to give the VGA out.) However, if one of your monitors will accept DVI digital signals and the other VGA, add a card with one of each of these connections and a DVI cable to match. (This is an if needed extra; many monitors still ship with only a VGA cable.)
Then turn off your computer, open it and add the video card. Install the drivers with only one monitor attached. Then power down the computer and connect the second monitor. Turn on both monitors before turning on the computer again. Most of the time, the second monitor should be recognized (by Windows) and the appropriate refresh rate and resolution chosen. If not, you may need to enter the Display settings to set the monitor up.
I have seen some computers/video cards where only one output is initially enabled. You may have to go into the device settings to enable it. (Laptops often need their external video ports enabled in the BIOS.) Bad video ports/cards/cables do happen so RMA if needed.
The USB video adapter, http://www.newegg.com/Product/Product.aspx?Item=N82E16812225007
, can be added to a desktop to give a second VGA output but it isn't the best solution. USB bandwidth limits are significantly lower than those for a PCIe x16 slot or an old AGP slot.
I hope this helps. Please add more information about your system if you want more assistance with this problem.
(who has done dual monitors with older and newer computers. My old Pentium 4 with a Radeon x1350 video card was fine for driving a VGA monitor and an HDMI monitor (using a DVI to HDMI cable). My second generation i5 and P8Z68 motherboard system is also fine using the on-CPU video graphics for those same monitors. A video card would improve gaming but isn't required.)