Before jumping into splitters it would help to know what cables are available for the monitor. Some monitors have multiple input capabilities and can be attached with an hdmi cable, vga cable, hdmi cable. For instance if there's an hdmi video out port on the back of the pc and an hdmi port on the monitor, an hdmi cable can be used to connect one of the monitors that way without need for an adapter. It varies from monitor to monitor as to what ports it does or doesn't have. If you have one that has only a dvi cable for instance, and your only other connector on the motherboard for the additional video connection is vga then yes, you would need the appropriate adapter.
+1 to gbb0330's question, some companies have an it (computer) dept or 3rd party contractor that handles those things. If it's a small company and you have nothing like that then hopefully the above helps you out. You don't want a splitter, a splitter will send the same signal to both monitors and you'll have 2 screens showing the same thing. You need 2 separate video outputs on the motherboard (aka 1 hdmi, 1 vga) and each one will have a cable to monitors 1 and 2. Then you can use extended display to span the screen across both monitors.