You can know the basics. If you can see or feel the ribs and hip bones easily, it's malnourished. If you gently pull up the scruff (skin at the back of the neck near the shoulders), when you let go the skin should spring back into place quickly. If it's slow to go back, the cat is dehydrated. A healthy cat will have a well-groomed coat - missing patches of hair can mean anything from digging at fleas to mange. If it will let you open it's mouth, you can check it's teeth. Also, white gums can be a sign of gum disease or anemia. The obvious thing to check for is fleas and ticks. Even if you don't see them, you may see the nits (will look like little black dirt balls) if you stroke the fur backwards.
I always tell people if they want to take in a stray, you shouldn't just take it into your house, especially if you have other pets. There are a lot of internal parasites you can't see and diseases which they can spread to your other pets. Even if it looks healthy, you should take it to a vet and have him do a complete physical.