Some programs advertise that they require no mortgage insurance. The more correct terminology would be self-insured. These programs actually have MI rates added into the interest rate and the lender will typically eventually get MI for them indirectly. There are some advantages to these programs: the MI portion is tax deductible as interest, whereas MI itself is not. And the lender is often willing to approve certain things that MI is not.
There are two basic payment plans for MI: monthly or up front. The monthly is paid, as the name implies, monthly. Payments are a set amount and do not change over the life of the loan. The up front option requires the first year to be paid in full at the close of escrow. This first premium is typically at a rate a little higher than the monthly rate. But the subsequent years are at a lower rate and thus save money over the long term.