In no particular order...
Security systems are either local or remote. That is, they either make a hell of a racket locally, or they make a phone call to a remote monitoring site; or both. Generally, if you have a remotely-monitored system, you can also have a local alarm set to go off.
Central stations (monitored) cost more; there is a monthly fee involved and a contract. They generally require their own equipment, and their own installation. You can get discounts by signing longer term contracts. You can also get a discount on your homeowner's insurance in some cases - check with them.
Alarm responses in the case of monitored systems are up to you. They can call police (or fire, if a fire alarm is triggered; or ambulance if a medical alarm is triggered) or they can call you first - or some companies send their own private security people or contracted security response.
Alarms are of various kinds. Glass break, magnetic contact, motion sensitive, photo-electric beams, and so on. The most common are magnetic contact, glass break, and motion sensitive. Also there are fire (heat) and smoke detectors.
We live in a small town. So we want police response, and we want them called first. Be aware that repeated false alarms can incur a fee from the local law/fire/medical emergency responders, so check with them.
We have pets, so motion sensitive alarms are not for us. However, glass break and magnetic switches are useful. If you don't have pets moving about, motion sensors can be cheaper and cover more ground than the others.
You can have keypads installed in strategic locations; we have one upstairs and one downstairs. You can have special keypads which offer specific buttons, such as 'panic' buttons for intrusion, fire, and medical emergency.
You can also have remotes that a person can wear. My 82-year-old mother-in-law lives with us, so we might consider getting a remote for her in case she should fall or something when we're not home.
There are security codes that have to be punched into the central keypad in order to turn the system off or to disarm it. There is a security code to be given to an operator if you accidentally trip the alarm and wish to not have an emergency response. You can create temporary codes for house-sitters and pet-sitters and that sort of thing. You can have reports created of who comes and goes and when based on their codes.
Basically, the entire thing is built around a core, and you want to think about what level of threat you wish to defend against before you invest in anything. Consider your exposure and your risk. Central monitoring is not really cheap, but it can give real peace of mind as well as a discount on insurance costs.
Don't forget you can check your exposure to risk also by looking at demographic stats on websites like
www.citi-data.org and simply by talking to police officers at your local PD or precinct (talk to them one-on-one, not at the desk. They often can't say what they really want to say when they are monitored).
Check out the alarm company. Name brands can be important, especially if the low-cost no-names are not going to be around in the long-term and leave you with alarm equipment that other companies won't use (they love to demand that you use their preferred brands and models, meaning buy it from them or you can't use it). Don't be afraid to test them out.
The sales guys are very much like car salesmen. They don't like to give prices, they like to set appointments and come over to your house and scare the bejabbers out of you. You need a negotiator on your team when they show up. Prices are all negotiable, so you must negotiate or get ripped off.
http://www.homesecurityguru.com/dont-get-scammed-on-home-alarm-system-quotes
http://en.wikipedia.org/wiki/Burglar_alarm
Now, currently I have a unique situation. I have a house in NC but an apartment in MI. I have devised a fiendish DIY security system for my apartment. It's very geeky, so YMMV.
Basically, I have a very small cheap old PC that runs all the time in my apartment. It is connected to the internet via my cable modem. I have two USB webcams connected to it, and it runs Linux as an OS and a security system called 'motion' which simply detects motion and then does whatever you tell it to do when it detects it.
So I have mine configured to send me an email and post the photo on Flickr if it detects any motion. I obviously can't rush to MI from NC and do anything about it, but I could call the police if I got the email quickly. If not, perhaps I'll have a record of who did it for the police.
Example:
I asked my apartment management to send a bug sprayer guy into my apartment while I was gone. I see that they did. You can click on the photo and see the photo larger. Not bad for a cheap webcam and a home-brewed system.
And yes, I'm paranoid. The real question is whether I am paranoid enough.
Hope that helps. I'll try to answer any questions you have.