My youngest hated to have his teeth brushed. My pediatric dentist told me to brush his teeth REALLY good at nighttime. We used kiddy toothpaste and sat on the couch with his head in my lap so I could see EVERY tooth I brushed.
He had all of his teeth and a small mouth so I had to really check to make sure I brushed every tooth surface due to crowding.
He could have an extra toothbrush but the PARENT brushes teeth until the kid can write in cursive for greater control of the toothbrush.
Also, make sure you have gone to the dentist already and go every 6 months. Many insurance policies only make dental visits mandatory after 4 years of age. They do still cover younger kiddos visit, you just fill out the enrollment paperwork earlier!
Mine still HATES the dentist but it is a requirement. Even though I brushed his teeth more than his older brothers his first checkup at 24 months of age had 8 cavities--he inherited bad teeth genes from BOTH of his grandmas, UGH!! After a $500 co-pay due to anethesia requirements (military dental program co-pays are terrible if an actual cavity is found) we go every 6 months and I am still his tooth-brusher 3 years later and for at least 3 more years. (Until he can write in cursive).