Organic or natural fertilizer can come from several sources, just remember that it must be well composted or your plants could burn or die. Cow or steer manure is the most common natural fertilizer, it is easy to acquire, comes in prepackaged bags and is already composted and weed- free.
You can collect your own cow or horse manure and compost it yourself, but you must make sure the compost gets real hot. Animal manure mixed with enough high carbon material, heated to or above 140 degrees F, for several days, is sufficient to kill most pathogens, diseases and weed seeds and to break down the raw material into something the plant can use.
Horse manure is not as digested as cow manure, because the cow has four stomachs where the horse only has one stomach. Therefore, more weeds are present with uncomposted horse manure.
Chicken manure is another organic or natural choice, but it is a very "hot" manure, high in nitrogen and urea and must be very well composted before use.
If you have access to fresh manure, you can either compost it or simply rototill it into the garden soil in the fall, giving it time to break down before spring. However, you will still have weed seeds to contend with since it was fresh manure. Composting is still the best way to go. Mix some straw or hay into your compost bin for extra phoshorus and a little sawdust for potassium.