How to connect two computers to one monitor

I have a monitor with one DVI input but I have a PC and a MacBook Air.

I have the cable to convert the Macs output to DVI which works fine but I don't want to have to keep pulling out the monitor cable to switch displays every time. I'm looking to have some sort of switching box that I can just flick a switch on.

Some monitors have multiple input possibilities and it is possible to select e.g., PC1 or PC2 for input. Check your monitor for this.

If it is not possible then you can use a KVM switch to switch your Keyboard, Mouse and Monitor between different machines.

If the monitor only has 1 input as you have described then you will require a Video Switcher often known as a KVM Switch. An example is linked here.
This also means that you will be able to share 1 keyboard and mouse for the 2 computers although if you prefer to keep the 2 (A better solution for a MAC + PC combo as in your case) then you can.

From the hardware point of view, you may try to purchase a Monitor Switch e.g. Belkin Switch2 KVM, Belkin SOHO KVM Switch or some cheaper version TRENDnet 2-Port USB KVM Switch Kit. It's also called KVM switch.

From the software point of view, you can use:

• use Remote Desktop for Mac to connect to Windows
• install VNC server on Windows and connect it via VNC client for Mac,
• you can use X11 services which will give you the same access to multiple systems at the same time each within its own window/frame (for Windows you need both X11-Server and Client installs, see: Xming or X-Win32). Read more details here and here.
• alternatively use remote desktop services like LogMeIn, Join.me, etc.