Once you have the NVC case number, which is the number you will use from now on, it can be tracked here https://ceac.state.gov/CEACStatTracker/Status.aspx?App=NIV
This will tell you when the NVC sends your case to the embassy, it will show as "in transit". And when it arrives at the embassy it will eventually update to "ready"
For k-1 visas you change the drop down to immigrant visa.
You can typically contact the NVC through the public inquiry form between 30-60 days after USCIS has said that they have sent your case to the Department of State. You can see that status through your USCIS account if you set one up, or using their case status tracker.