There is a fine art to internet stalking. The key is to find out information and yet not go so far as to hack their facebook passwords and read their private messages and do illegal bad things. You just want to find out what kind of information is publicity available about the person.
I think I'm actually fairly good at internet stalking...it's the combination of persistence and research skills. So I'm going to share some tips but also tell you why it's good and why it's bad to internet stalk people.
How to find someone if you know their first and last name:
First, start with a basic google search. This should be the beginning of any good internet stalking. We geeks are all familiar with google but play around with the different advanced google search settings. Things like "" are very important and can make a huge difference when searching.
Try common social networking sites to see if they're on it. You can try facebook, myspace (if they're like a weirdo and haven't switched to facebook yet!), or linkedin. A lot of these sites will also include pictures so you can confirm to see if it's the right person. If the picture is of like a dog or a tree, you might look at the friends list and see if it's someone they might know (particularly useful for finding old classmates.)
Other sites you can try are pipl, spokeo, and zabasearch. This is more useful if you want to find out information that's in their public records, places they lived, approximate age, scary scary things like that. Put your own name in and you might be scared at how much info people can find out from the internet...and yeah it might be not be 100% accurate but generally it's accurate enough to be scary.
What to do if you know their email:
You can try to google it of course, but also try social networking sites b/c sometimes you can search by email. Unless they used a different email when signing up.
What to do if you just know what they look like and have a first name:
And yes I totally found someone this way... I had a first name and I knew what they looked like and I knew where they worked and I found them on OkCupid. Granted I knew they were on OkCupid but still, considering OkCupid is not name searchable, disturbing in many ways. I googled the first name and the workplace and found public information that seemed plausible. Approximate age etc. It gave me a last name to search too. But on OkCupid I just put in the age, ethnicity, and probable location and just had to search through maybe 2 or 3 pages of results? Totally creepy and stalkery but it did work.
Anyhow, you can see how the combination of a little bit of information can get you pretty far.
Some of you may be asking, how can I avoid being found on these searches? Well don't put anything on the internet. If you have public facebook, linkedin page or flickr account tied to your actual name, you're that much easier to find. You can use a nickname or pseudonym on social networking so your friends might be able to find you, but be aware that if someone knows a friend of yours, they might be able to track you through them. I was actually found on LiveJournal this way. A friend of mine was googling our mutual friend and she found my account linked to hers! In this case, it was a good thing but you can see how you might not always want people to find you online. A smaller internet presence helps you hide.
You can also avoid buying property or other things that might trigger public records. What's weird is like on spokeo they don't list the house I actually purchased but my parents house. So yeah, not a 100% but still creepy.
I would like to reiterate that it's very important to control your online presence. Google yourself periodically and see what can be found. Make your social networking sites information private and only available to friends. Use alternative emails and names when signing up for things on the internet. This can protect you from stalkers but also for more mundane things like keeping a future employer from seeing photos of your drunken escapades at a bachelor party.
Why Internet Stalking is Good:
B/c as nerds, sometimes we're too shy to find out things from people directly and we want to do some research ahead of time. I know I love doing internet research! But internet stalking is a way to find someone that you might be interested in talking to more but totally couldn't do it at the social event or you just plain forgot to get their contact info. Basically the less work you had to do, the less creepy it is and it's more likely they'll talk to you. Unless of course they're flattered that you did all that work b/c you were interested. It's really a fine line between flattery and disturbing--tread carefully.
Sometimes you also find out useful information...like that bastard is already married! There was a news report about how recently a woman facebooked her husband and discovered that he had gotten married...again! You can also find out if they're drinking when they aren't supposed to (Lindsay Lohan), that the purse full of drugs they said wasn't theirs totally is (Paris Hilton) etc etc. They say they don't have kids but surprise, they totally are crawling with babies in photos.
Why Internet Stalking is Bad:
But again, like with any power, there is responsibility.
You need to not stalk your exes. It doesn't help anybody to find out too much information about your exes and pretty much anything you find out is going to feel like a kick in the gut, especially in the early stages of breaking up.
You should never hack someone's account by trying to guess their passwords or whatever. It's immoral and serves no purpose other than being a jerk. You going to spy on them? Change their information? Make them realize that they do love you? Not going to happen, keep your integrity. Don't do it.
B/c nerds never need more excuses to obsess over things. We examine the minutiae of like everything. I don't think trying to find out what elementary school someone you haven't met went to is going to lend itself to great insight into the viability of your future relationship. Don't over think it, just be chill.
And along those lines, back to over-analyzing. You've spied on someone and you've found incriminating pictures (or information) of them. Dun dun dun! Who's that girl? Whose baby is that? Why does he look really really red in those pictures? Well don't break up with them just yet. We know a lot of people are internet liars, but don't go searching for excuses to ditch the dude. Don't jump to conclusions...that baby could be their niece or friend's kid (if they said they're childless) and that girl could be a sister or cousin or just a friend. That redness could just be a really bad sunburn. The thing about information on the internet, unless you're reading their diary, pictures and such are context-less. You don't know what happened before or after.
So yes, there are benefits and downsides to internet stalking. Use this power wisely and don't get carried away. But I think the most important lesson is to control your own internet information so embarrassing pictures like:
don't get spread around the internet.
*When I'm talking about internet stalking, I'm not referring to the creepy illegal kind that warrants a restraining order. I'm talking about stuff that an employer or future date would do to find out what kind of person you are. If you're doing the bad kind, you suck and you make us all look bad and I hope the cops arrest you.
In the beginning of a relationship, it's really easy to get caught up in the smooshy faced romance of it all. You want to be around them all the time, you want to know what they ate for lunch. You want to make out constantly. Again, that's great--for you two. If you don't know how to keep your lovey-doveyness in check, you're going to want to make your friends vomit when you tell them about how cute your new bf/gf's toes are. 
If your friend is dating a bum, you can try talking to them but likely they're going to be irrational and not do anything about it even though they probably complain constantly. I've tried staging interventions (we did everything but the sign!) and that didn't even work. So tread very carefully in this arena.