Hello Ashley!
In Italian we have our way to say it but it's not exactly like english :)
The most common expressions are:
"I'm going to start/to do the laundry"
- Sto cominciando a fare il bucato (but it is literally "to start doing" it is a WORK IN PROGRESS)
- Sto facendo il bucato (I'm doing it, I'm in the middle of the action)
- Sto lavando i panni
- Ho messo a lavare i vestiti sporchi (dirty clothes - this is a "passato prossimo" action. We use passato prossimo to describe a recent past or a past that is still connected with the present. This expression means that you did it recently or that you started it and soon you'll have to take them off the washing machine)
Anyway these are the most common ones! I hope that I've helped you :)