How to build a cheap bird house
Some birds are cavity nesters and will use a house that you build. Some birds need bushes and trees (native to your state), others nest on the ground. All do not tolerate weeds. Yes, leave the weeds and you'll have less birds, more rodents.
You can build all sorts of fancy birdhouses, or nest boxes, but the birds really do not care for fancy, they prefer simple, natural, and rough nests. They nest in holes in trees remember? Wild birds do not hire a wild land Realtor.
When you start looking around there's all sorts of junk wood laying about. 1X6 cedar or redwood are probably best, but we've used 1/2 or thicker exterior plywood, OBS and pine before. The wood needs to be old and rough. Smooth particle board, metal, or plastic are not good. No paint, natural. The dimensions do not have to be perfect. Close is usually good enough. So if you do not have anything but a screw driver and hand saw look for wood that is close to the right thickness and width to start. A box that is an inch too big or small will still probably be used, if the hole is the right size and the right distance from the bottom.
Placement of the boxes matter, put the boxes where birds want to be. Put the bird house along the edge of the the woods, on a fence, house or tree facing an open area with the hole pointing away from spring winds. This is usually south.
A picture showing the dimensions.