How do I separate contacts from work and personal Google accounts?
You can download Google Contacts app.

When you want to switch accounts, just tap the profile picture thumbnail on the top right, and select the desired account.



You can select either Google account, or view an unified list (for whatever reason, or if you later change your mind)

When adding a new contact, make sure that you are selecting the correct account. (you can view it at the top as Save to)

Of course, both accounts need to be connected to the device, and sync should be enabled.

And if you mixed up your contacts...

From your comment:


  [...] it seems that the phone's contacts are syncing to both accounts. [...]


You can switch accounts to confirm, and if it happened, you may want to delete the duplicated contacts, and then switch to the other account and move your contacts to the right place.


Select the contacts you want to move (tap and hold)
Press the menu button (or the three dot menu at the top)
Select your desired action:


Select all
Delete
Move to another account
Add label (Group using tags)



For more details, you can visit the google contacts support site.