I always look at various pictures etc.
A lot. Internet, some books, but mostly Google, wikipedia + a lot of press of course
i am constantly reading books and checking art shows out etc. Sometimes i don't like to look at any work as i don't want to be influenced by certain trends and styles. i go through stages of getting a lot of material then i don't.
I do life drawing (almost) every week, and carry a sketchbook around with me pretty much wherever I go. I do studies from movies, books and magazines, and push myself to try new media with translates into digital in new and unexpected ways.
I photograph all the time, building a digital file; roughly a terabyte drive. I have an old fashioned Morgue file in 4 filing cabinet drawers on every subject under the sun. I keep saying I'm going to scan them in, but it's a daunting task... i need an intern. I also do the Google search on keywords and see what turns up, but I rarely snag anything that's not mine. I will study it, but then draw without looking at it.
Mostly I have to look up objects that I don't have locked in my memory (animals, clothing, weapons, etc.) For larger works, I will sometimes have to look up histories and philosophies to get in the right frame of mind. This sometimes results in hours spent on wikipedia.
I try not to steal ideas or use too many references, I prefer to dig into my imagination but I'll always do bookwork, historical research, design research or failing that dive into internet image searches to pull out references where I absolutely have to use them.
A lot, especially if it's not a subject matter I'm familiar with. Visual and contextual research are both important, looking at time periods, target audiences, the company the illustration is for, etc.
Whatever is needed!
I mostly use Google Images, flickr or other photo repositories for image reference but sometimes take my camera out and take my own photos.
Museums, wiki and lots and lots of reading.
i'm a research freak. a quick research on net to start with, end up reading a few books in related subject or interviews.
Curling up in a big, comfy chair and looking at various comics and picture books is not only a great way to study illustrations, it also gives you a nice cozy feeling in the pit of your stomach. It's best to do this with a mug full of milk and several cookies near you. This creates a relaxed atmosphere, which makes it easier for me to retain what I've seen.
Sometimes the work doesn't require any research, but most of the time I try to find pictures with the right mood, be it other people's illustrations or art, or just nice photos or colors.
Google and Flickr mostly.
Online and visual research. Then the sketching begins...