Parakeets are small and gentle birds and most of the time they actually do not get sick often with proper care to their needs. Sometimes it can just happen though and you would definitely know if your parakeet is sick. The main reason a parakeet bird would get sick is because of a poor diet. Not enough nutrition is really dangerous for them since they have a delicate digestive system and need all the nutrients that are recommended for them. Sometimes their sickness is formed from stress believe it or not, and this is probably due to a very loud environment which they are not too comfortable in.
At times, it can be hard to tell if they are sick because they won't show any major signs at first. A common sign is if they look a bit lethargic, not chirping and tweeting as much as they used to is also pretty common. Another almost sure sign is if they do not want to perch as often. They could be found at the bottom of the cage with a certain weak air around them. If they are not eating as much as they used to, this is a sign of a lost appetite and if it prevails, they definitely seem to be sick. If they look sleepy most of the day and have no signs of their appetite coming back you are most probably dealing with a sick parakeet.
Before taking them to the vet, which mandatory when a bird catches a sickness, be sure to keep the room they are placed in at a warmer temperature. This will make them feel more comfortable since cold air would make them even more sick. Don't make it too hot though this will also bring some discomfort for them. Also try to feed them foods high in calories, even if they are not too hungry, this will give them back most of their strength and keep them at a better comfort level. It's essential for them to gain back their strength to help fight off their sickness.
Also make sure the room is quiet as much as you can get it. A sick bird needs rest and relaxation, loud noises will only cause stress on them and this would make them feel even worse, it can also be fetal. Keep the room quiet with dim lights and they should find it much easier to sleep and keep warm. Taking care of a sick parakeet should only be a day or two because they do need immediate vet attention to see what the problem is. After the vet visit do as the vet advises you to and make sure your parakeet stays in the utmost health.