First, read your new policy cover to cover. Every July when ours arrives, I find that they've added a few things to my policy -- things I may or may not be willing to pay for (for example, towing insurance; I've had a car towed exactly twice in my life, and it's not all that expensive -- not something I need to have covered by insurance). If you find that this is true, before you begin paying, call your agent and have those specific things removed.
To keep your bills low, consider these tactics:
1. Pay every 6 months or every year. Paying month-to-month costs more.
2. Bundle your car and home insurance into the same policy. You get a better rate for both.
3. Don't jump from company to company. Instead, find a good company with reasonable rates and stay with them. I've been with the same company since I was 16 years old, and the discount for longevity is worthwhile.
4. Raise your deductible. This places more risk upon you, the consumer, but it slashes your premiums. The deductible is "might have to pay" money. The premium is "definitely have to pay" money. I've had car insurance for more than 30 years, and I've never once had to pay the deductible -- sure, this might be the year that it hits me, but even if that happens, I've had enough years of saving that it's still worthwhile.
5. Do not over-insure yourself. That is, don't get sucked into the idea that you must be protected for absolutely everything that could ever possibly happen. For example, we don't carry comprehensive insurance on the 1999 Ford that our daughters share; it's literally worth nothing, and if it were to be wrecked today, we have the resources to replace it with another used car.
On the other hand, don't go too far the other direction either. Be sure that you have enough coverage to manage an expensive problem, if it should occur. Be realistic about what you need in the way of coverage.