If You Don't Know Your Target's Name
Let's assume you want to search for someone whose name you don't know. Say you got a random phone call at 4 a.m., or someone has been spamming you with a certain e-mail and IP address combination, or you really want to find out who that jerk is on the forums you frequent, who goes by a particularly unusual handle.
Phone Number/E-Mail Address
Most services that offer phone number lookups also offer a reverse phone number lookup--in which you input a phone number to get information about the person calling you--for a nominal fee (usually around $5). However, this information can be inaccurate--as I pointed out above, an initial reverse phone number lookup on my phone places me in South Carolina.
One of the best places to do a reverse phone number lookup--and a reverse e-mail lookup, while we're at it--is Facebook. While you can't look people up by phone numbers (even if they have it listed on their profile), you would be surprised at how many people leave their numbers on their friends' public walls. If you search for a phone number on Facebook and it's been left on someone's wall (or on one of those "I lost my phone, need numbers" group walls), it will show up in the search results.
As for e-mail, well, you can search for people on Facebook by e-mail address. And even if their e-mail address isn't publicly available on their profile, if it's in any way affiliated with their profile it will show up.
Also remember to plug phone numbers and especially e-mail addresses into Google, as people tend to slap their e-mails publicly around the Net without even thinking about it.
If you know nothing about the person you're trying to look up except for their username or online handle, fear not. So long as the username/handle is reasonably unusual, you'll be able to find a decent amount of information (which you can then use to perform other searches).
Pipl is an aggregator that searches the "deep Web," or parts of the Internet that are often missed by regular search engines such as Google. Pipl allows you to search by name, e-mail address, username, or phone number. Pipl then crawls the Web and aggregates all search results that contain your terms--so it's more of a one-stop shop for results.
Pipl is excellent for hunting down information about people whose name you do not know (as for people whose name you do know, it mostly just finds what you can find on Google and social networks). The username search is particularly useful, especially because a lot of people use one handle across the Web.
Other aggregator sites also exist, such as ZoomInfo, which aggregates job and company information; iSearch; and Wink. Unfortunately, aggregator sites can be as much of a pain as they are a convenience, as they often confuse people and spit back a mix of related and unrelated results.
Web Domain/IP Address
If you want to find out who owns a domain, the process is pretty simple. The Whois database keeps a record of all domain registration data, and you can search it via a number of sites. Whois.net and Whois Source are just two sites that allow you to look up the registration data for any domain, and, if you're lucky, figure out who the owner is. Users are required to provide an address and a phone number when they register a domain. Of course, many Website owners opt for private registration, which hides their personal information.
You can also look people up by IP address on Whois. You can use tools such as Geo IP Tool to search the Whois database and find out some info on the IP, specifically where the person is coming from. For example, my current IP is 18.104.22.168. If I enter this information into Geo IP Tool, I can see that I'm located in New York, New York, zip code 10019. Sure, that's not enough to be able to find out my phone number, but it's a start.
While Web domain and IP address lookups may seem like a dead end, they're often just the start of your search. If you can gather any information from the Whois database, you can use what little you know to aid you in your further searching. For example, if you're looking for me and you find out that I'm located in New York, thanks to my IP address, you can probably disregard the search results that put me in other places.
Well, there you have it, folks. Go forth and stalk yourself without spending a bundle. Have your own people-finding tips? Leave them in the comments!