Very carefully is generally the manner in which it is painted...though that really isn't much help. Most methods of painting it are variations of the same method - they all come down to steady brush control, patience and practice. However...
...you can cheat. I used to fret about with getting straight lines and square edges, but have since switched to decals.
It still takes a bit of practice and patience, but luckily...when you goof - you just wash the old decal off and start over. Much less frustrating. On most miniatures you will need to use a fair amount of decal solvent (Micro-sol) - but it isn't all that hard to do.
Start off by finding a decal that has the particular checker pattern you are after, size and colors. If you do not find anything - you can print up a sheet of your own easily enough. If you want white as one of your colors - simply paint the area white to start with and then apply the decal over that.
Cut a section of the decal out that is a little larger than what you are planning on covering. Float it per the directions and use a brush to lift the decal and slide it in place. Apply decal solvent with a second brush and slowly ease it down over the curves. You want to keep it from drying out while you work. If a curve is too tight, you can ease it a bit by making small cuts - these may need minor touch ups with paint after the decal has dried. Once it is down, while it is still somewhat wet - use a scalpel to trim the excess decal off the edges (trimming while wet with a sharp scalpel prevents the decal from flaking as often happens on dry decals).
You can usually put down a decal in less time than it takes for the first color of paint to dry - and it ends up being extremely crisp lines which are very hard to achieve with a paint brush.
http://www.microscale.com/Merchant2/merchant.mvc?Screen=PROD&Product_Code=MI-2 - Just in case you weren't familiar with decal solvents.
http://www.1999.co.jp/eng/10032073 - As an example of what I am talking about. That isn't the best example, but it was the fastest that I could grab a link for. You can find full sheets of different patterns that are sold for the modelling hobbies like model railroads and fine scale aircraft modeling. In addition, they have patterns like the banded caution stripes and even tartan patterns (for scale figure modelers).