Net 60 simply means that the balance is due in 60 days after the invoice date.
The 30 day invoicing is a little more complicated, but still rather simple at the same time. It simply means that the invoice is done in 30 day increments regardless of how many days or in the month. Many times you think you have a bill due in one month, for example, say you get an invoice dated January 31st, and it's due NET30, many might think it's due the end of February, which has only 28 days in it, the bill would actually be due on March 2nd, 30 days after.
The same holds true for months with 31 days in them, if the invoice is billed at the end of the previous month and the next month has 31 days in it, the invoice is due on the 30th, not the 31st.
Basically you count the literal 30 days from the date of the invoice, so for Feb once you got to the 28th, you'd start with March 1st and so on.