I found a fledgling that had fallen out of the trees today. But although I normally put them back in the trees, this one had a small abrasion and a wee bit of blood above its eye. So I have it in a crate, with a container of water and it is alert enough that I have been feeding it soaked cat food. However I have never dealt with Pigeons before and dont know if it is shutting its eyes to sleep or because it's sick. Can I please get some urgent advice on how often I need to feed it, whether I need to drip feed it water or when I will be able to release it back to the wild.
We really need to know the age of the pigeon to give the best advice. Posting a pic, or describing it as best you can would help a lot.
As biophiliac correctly said above, cat food is not what you want to feed a pigeon.
If it is fully feathered, or almost fully feathered, it will eat pigeon feed (mix of peas (maple and/or vetch), millit, corn (not cracked) and maybe sunflower seeds). Even if you can only find one of those types of ingredients it should suffice, but they do best on a balanced diet. However, at young bird ages pre-wean (so about 2 weeks old to a month old), while pigeons do fine on grain mixes, they may not know how to forage yet and are still relying on mom and dad to feed them. I have found one good way to encourage young pigeons to forage is by sprinkling some feed on the ground nest to it and taking your finger, as if it's the beak of a feeding bird, and smack it down on the pile of feed as if your finger is eating it. The baby bird should watch and be inclined perhaps to do the same thing with its beak and attempt to eat.
If it is not fully feathered or close to it, and is still covered mostly in down and undeveloped feathers, it really needs its parents to feed it, or for you to feed it. If that is the case, look up videos of feeding baby pigeons using syringes and other methods, and a combination of either store bought baby bird food such as Kaytee Exact, or homemade pigeon milk such as "MacMilk". With this method, keep in mind that baby pigeons do not eat like most other birds having soft food regurgitated
into their mouths, but, rather they actually
reach into their parents' mouths and eat food from it. As such, your feeding methods need to account for this.
They should be fed when their crop is fully empty, and feed until the crop is about 75% full.