It is not unusual for a single female Cockatiel to lay eggs. Other birds do this as well, but cockatiels seem to do it more often than other birds.
Your female cockatiel does not have to be with a male to lay eggs, but the eggs that she lays will not be fertile – so there will be no babies hatching from them.
You may not even know that you have a female bird until one day you find an egg in the cage.
The number one rule is to leave the eggs with the bird. She probably will not sit on one egg, but if she lays a second one in two days and then a third in another two days, she may start to incubate at that time. She may not even lay the eggs in a regular pattern and may not even lay a second egg at all.
Leave her alone as much as possible to allow her to rest and incubate the eggs. Once the time has past for them to hatch, she will abandon them. At that time, you can remove them. She may lay another clutch soon afterwards, or she may wait a month or so and then lay more eggs. Cockatiels normally raise two and sometimes three clutches, one after another and there is a good possibility that your bird will follow this routine.
Each time, you should allow her to repeat the incubation process until she abandons the eggs before removing them.
Do not provide her with a nest box or a hiding place as this will just encourage her to lay more eggs. If she continues to lay eggs, there is the possibility of egg binding, which is very serious and could cause her death.
Provide her with a good and varied diet including cuttlebone and crushed egg shells to replenish the calcium that she uses with each egg.
She will most likely stop laying eggs after two or three clutches in a row. She may only stop for six months and you may have to adjust the lights to keep the days short for her to prevent excessive egg laying.
Once she stops laying and inclubating these eggs, she will be back to her normal friendly disposition and will want to be with her human again.