Step 1: Sepia Tone
Open your image up and go to Image>Adjustment> Photo Filter. From the drop down menu select Sepia and increase the density. Click OK.
Step 2: New Layer
We are going to add our first bit of colour to the image but we are not going to paint directly onto the photo layer. Click on the new layer icon or go to Layer>New Layer and change the blend mode of the layer to Color. This is so we can still see the shapes, shadows and tone of the original image through the colour we will apply.
Step 3: Paint
Select the Paintbrush Tool picking a size that's appropriate for the area you're working on. Try using a brush that's not too hard and you can change the colour you're using by double-clicking on the foreground colour square at the bottom of the tools palette. Then simply start painting. If you're going for the hand-painted look then you don't have to worry about being too precise.
Step 4: Opacity
If you think the colour's a little strong simply reduce the opacity of the layer then create another new layer and repeat the above steps for each colour you apply.