I want to get my child's EEG done. How do I proceed with that?

Speak to your doc. Speak with your child's pediatrician about why your want your child to have an EEG.
Family MD. Your local md can set up your eeg for your child. If possible, try to get it scheduled, performed, and read by a pediatric neurologist. Preferably a pediatric neurologist with specialty in epilepsy can evaluate your child if seizures are found on the eeg.
Prescribed testing. The various labs available for such testing require a doctors order to set it up.They also need some history and details on why it is being done/different types of EEG's (standard/overnight/video-monitoring/etc.) Iff you are ready, call your doc and get it set up.