This is the least expensive trap to build. All you would need is a three to five gallon plastic or glass jar, a wooden plank, about two cups of perlite or shredded Styrofoam, some grass seeds or sunflower seeds, and water. The bucket should be clean as scum probably would allow the rodent to climb out.
A little peanut butter applied to the rim of the jar or bucket would attract more rodents.
Wild rats, especially Norway rats, are much more cautious than mice. They might climb to the top, lick off the peanut butter, and then run away avoiding the trap altogether. We had more success using the Havahart live trap, but those are much more expensive. http://www.havahart.com/store/animal-traps
Norway rats are huge. Adult rats can reach eight inches long or more, not including their tails. I have seen them jump from the bottom of a small five gallon bucket, so you may need to use a large garbage bin either a 15 to 20 gallon bucket or more to trap them. We live in the foothills, so Norway rats are imported from building sites, usually home renovations. Therefore, with these huge rats, the water level in a bucket should be increased to at least ten inches so that if an 8 inch long rat fell in, it would stay in. About two tablespoons of unscented laundry detergent added to the water would break the surface tension so that a rat and its fleas would not survive for very long. In addition, detergent would also make the sides of the bucket slippery and easier to clean.