Don't be tempted to try to build your own. It just is not possible for you to make one that is as sturdy and attractive as a factory produced cage. Cages are really very economical these days. If you start adding up the price of all the paint, wood, and hardware that you would need to construct a cage, you will see that it is much cheaper to buy one. The cage must be at least long enough for the parakeet to stretch and flap its wings.
Parakeets also get a lot of exercise by climbing on the bars.
Make sure that the bars of the cage are close enough together, so that the bird can't fly out or even stick its head out. If your pet sticks its head out through the bars, it might get its neck caught and choke to death. Today's modern cages are made of metal and plastic. Don't put parakeets in a wicker or bamboo cage. Cages come in every color of the rainbow.