First you need to choose a picture to replicate. A pet or favorite animal is a great choice but don't limit yourself, there are lots of other subjects that will work just as well. That said, a distinct outline and a decent amount of color variance will produce the best results.

With your image in hand you'll want to start by removing the background. Special apps, like Background Eraser, and high end software will make quick work of this but getting stuck in with the erase tool in Paint is also a viable option. When the background is gone you can begin dividing up your subject.

Start by tracing the outline with straight lines. Next, if your subject has distinct color sections trace those, otherwise use the vertices of the outline as starting points and begin drawing triangles. Be conscious of your mesh size as too small of triangles will cause your piece count to soars, along with your workload. On the other hand, go too big and you lose too much fidelity, making it harder to interpret the final image. You can see in the animation below how my initial mesh (green) was very tight and I ended up redoing it to it's final, 109 piece, size (yellow).

Now that you have a mesh it's time to choose your colors. While I could have gone with a couple more shades of grey to get an even closer match I instead decided to really push the image's high contrast, one of the reasons I chose our dog as a subject in the first place, by only using three main colors. How much time you want to spend mixing paint and how you want to paint (by-hand, spray, etc) should all be considered when choosing colors. The picking itself can be done manually with the software's color wheel or by using a built-in or plug-in "Average Color" tool for each segment.

Finally you need to print your template. You will need at least two copies, one for cutting and one for assembly/reference, but unless you have a large format printer or a small image you will probably need more. This is because you will need to Poster Print the file, if it's over 8.5"x11", and pieces falling on the seems will need their own printouts to be cut. Just make sure all prints are at the same scale!

Edit: Thank you to user AlexA214 for asking for the full scale template. I should have attached it from the start but better late than never. The .zip file contains both a .bmp and .pdf version of the full size template ready fro printing.