The big question you should ask right away is if your plan is considered "managed care" or not. If it is, you will likely be saving some money, but those savings will come at a price. Generally speaking, these kinds of plans are more restrictive in both the doctors you can see, and the procedures and treatments they can give you for your ailments. If you know this going in, it can save you some trouble down the road.
Another thing you'll need to find out is if you have the option of seeing a doctor outside of your group. Some managed care plans allow you to see a specialist, for example, who isn't in your group, but they require that you get a referral from your primary physician. Generally, if you do see a doctor outside your group, it is going to cost a bit more.
Another thing to be sure of is the approval process. Many plans require additional approval for prescribed treatments, even if they are suggested by your primary physician. If you go ahead with a treatment that hasn't been approved by your plan, then you may end up having to pay for the whole thing by yourself. This can get quite expensive, so be careful.
The last thing you'll need to be aware of is what kind of prescription drugs are available on your plan. Many plans only cover generic drugs, and it's important to know this. Some new drugs that are popular don't yet have a generic version. If your doctor prescribes you a non generic brand without knowing whether your insurance covers it or not, you will either have to pay for everything yourself, or go back to your doctor for another prescription. It can save you a lot of time and money if you know this ahead of time.
Long gone are the days of having comprehensive health insurance that covers everything. That's why you need to know what you're covered for, and what you aren't. That way you can be sure to maximize the benefits from your plan, and minimize the cost.