I am not sure if this is the right place to ask this question, but I guess that ornithology enthusiasts (or ornithologists) will have the best knowledge about it.
I am wondering if there is a website which would identify birds by their looks. For example, I would specify that the bird is similar to a sparrow in size (just a little bigger), it has a gray back and yellow-ish-orange-ish belly and it would tell me the exact species.
If you are on the go, the Merlin app for your smart phone is great. Especially if you are in North America!
Merlin is a smartphone app that you can download via your preferred app provider (apple, google, etc.). It is maintained by the Cornell Lab of Ornithology, and is related to the All About Birds online archive.
The app does exactly what you are looking for, where you specify the approximate size, up to three colors, where the bird was seen (in water, at a feeder, in trees or bushes, etc) and where and when you saw it and it can provide a list of suggested birds. The suggestions have information on identifying the bird species, maps of the species distribution, and example sounds that each species makes.
If you are an avid birder that records your sightings in eBird (also created and maintained by the Cornell Lab of Ornithology) there is an option to add the bird to your "Life List" from within the Merlin app.