Combine custom patterns and the Paint Bucket for easy results!
Create a new canvas with File>New at 30px by 30px. Zoom in and draw a grey Rectangle (U) around the edge. Go to Edit>Define Pattern. Enter a name and hit OK.
Create another new canvas for your full image around 1000px by 1000px in size. Select the Paint Bucket tool (G) and in the Options bar, change Foreground to Pattern. Click the Pattern preview drop-down and find your square will turn into a grid.
Change top drop-down back from Pattern to Foreground. Begin to use the Fill tool to colour the squares black to create an outline. If you make a mistake, simply fill the square in white.
Using the Paint Bucket tool, begin to fill in your outline with big areas of block colour, square by squrae. You can go back at any time and change the colour by simply changing your Foreground colour and re-filling a square.
When your main colours are in place, use the Eyedropper tool (I) to select a colour from a section. Double-click the Foreground colour preview and move the Colour Picker down to a slightly darker shade. Use this colour to add some simple shading around the edges.
Double-click the Background thumbnail to turn it into a layer. Create a new layer with Cmd/Ctrl+Shift+N. Click and drag it below your image. Select the Magic Wand tool (W) with Tolerance set to 100. On your image layer, click a background square and hit Delete. Fill the bottom layer with a background colour.