This bears repeating. Privacy is important, and Google+ has great privacy controls. But you need to know how they work to use them to best advantage.
The first rule of privacy on Google+: people don't get any access to your info without you
taking action. Relationships in G+ are "asymmetric", meaning you can "follow" someone ("adding to a circle", or "circling") without their having to reciprocate by circling you back. When you circle someone, the things they share you'd already be able to see anyway
— because they're shared publicly or with a circle that includes you — will appear in your streams. But if you go to their profile before and after you circle them, you won't see much difference — circling someone doesn't give you access to their info.
At the same time, when you circle someone else, you are not only asking Google+ to put that person's shares into your stream, but you're also giving them access to things you
share with your
circles. For instance, if you edit your profile (the circle with a profile in the buttons up top of the G+ web interface), you can give people in your circles access to your email address or your phone number. Those are people you
have added to your
circles, not people who have circled you. (When you edit your profile, you can change the visibility of items by clicking the little icon next to each one.)
Similarly, if you enable G+ chat, when you click the triangle to the right of your name in the chat box (in the left sidebar of your G+ stream, not
in Gmail) you can choose whether "Your Circles" can chat you, or a custom selection of circles. Note that those people must have also circled you and done the same; chat is obviously one case where reciprocity matters!
But if you've been paying attention, you'll notice that you circle someone for two different reasons: one, to see their shares in your stream, and two, to give them access to your info and/or chat. This makes sense most of the time; people you know are the people you want to hear from. But sometimes the two don't align, and when they don't, you need to know a couple of more advanced tricks, which I've taken screenshots of below.
First, not all circles are created equal. Some circles are ones you may use for celebrities or people you don't know but who publicly share interesting stuff. (A lot of people use the "Following" circle for that.) Maybe you want to get their stuff in your stream, but you don't want to give them any access to your info. No problem: go to https://www.google.com/settings/plus
and click "Customize" under "Your circles" (first screenshot). Then make sure only the circles you want to share with have the checkbox clicked (second screenshot). Now, when you see "Your circles", you know that really means "all my circles but the ones I unchecked here", and you're safe to add whoever you want to "just follow" to those unchecked circles without giving them visibility to things you want to share in a limited fashion.
What about the reverse case? Maybe you have business associates or acquaintances who post stuff you don't care to read, but you do want them to have the "always up to date" contact information in your profile (especially useful if they have an Android phone or use Gmail!) and/or access to chat you. In that case, put such people together in a new circle (I call mine "Contacts", because that's how I think of them). Make sure the circle is checked in the "Your circles" setting we just saw. Then go to your stream and click that circle's name in the lefthand sidebar (third screenshot). Now, at the top, you'll see a slider. Drag it all the way to the left (fourth screenshot), so it says "Show nothing from this stream in my main stream" (fifth screenshot).
Now you won't see this circle's shares unless you specifically go to this stream again, but since this circle is part of "Your Circles", they'll have access to the things you want to share with them.
(One final note: when you enable chat in G+, you have your choice between allowing chat from "Your Circles" and a custom set you select. This gives you even a bit more control. Maybe you don't want to be chatted by that guy you're following with the interesting but weird political opinions, but you'd just love it if your favorite celebrity were to respond to your insightful comment with a chat. It's your choice.)