What is the daily life of an industrial engineer like?

I'll answer your latter question first. Here is an engineering jobs website that might be useful. I'm sure there are many others. Read through some of the job requirements and you will also get an idea of what industrial engineers do in different industries.
http://www.engineerjobs.com/jobs/industrial-engineering/georgia/

"Industrial engineers work to eliminate waste of time, money, materials, man-hours, machine time, energy and other resources that do not generate value. Industrial engineering is concerned with the development, improvement, and implementation of integrated systems of people, money, knowledge, information, equipment, energy, materials, analysis and synthesis." I copied that from Wiki, but my point is it's a pretty broad field. Industrial engineers are usually generalists, but you can specialize.

A typical day back when I worked for GM in the '70s:
Walk the assembly line looking for safety and housekeeping issues. Address those with whoever you might need to help you get it done.

Go to the line schedule review meeting for the next day's/week's production. Ideally, you want a nice level rate of production. I don't mean a change in line speed, I mean a change in options. For example, back in the day when the paint job was totally manual and paints were more primitive, you saved paint if you could paint all the white cars in a batch (less purging of lines prior to changing colors). It took a team of 5 people to put on a vinyl top. Obviously, you can't have more than x of those in a row without adding either more people or equipment which requires space. So you compromise all the while trying to have a smooth flow adding resources as needed.

Later I worked in aircraft.

One large project I worked (with lots of help) on was to convert our sheet metal assembly building over to composites production. And, you cannot stop production while this is happening.
So, the problems was
Offload the sheet metal work. Build ahead and stockpile enough parts to allow the new vendor to get up to speed. IE did the calculations, figured out which parts had to be grouped (shared machines)
Do the layout for the new work coming into the building. Where to efficiently put the tape layers, layup/clean rooms, autoclaves, dirty areas (trimming and drilling, etc.) so you have a smooth flow and as much in sequence as possible without too much travel distance/space.
"Office work " I did was things like, selecting newer equipment. Calculating when we would need that 5th machine, and where to put it, now that demand has increased. Doing payback, ROI, and similar analysis. Developing metrics.

And so forth. It's been and will be for you pretty wide ranging.
I do want to mention, that people skills are very important. There's no way you can know about all aspects of production jobs. You have to be able to talk with folks whether its to get to the root of a problem or whether it's to try something different. You've got to be honest, build trust. And, you have to deal with/talk to different levels of the organization be it the hourly employees or the VP of finance that you are trying to sell you new machine idea.

The best part for me, was the project nature, variety, office work as well as floor work. A bit of both worlds. I hope I did not make it sound particularly hard or intimidating. I loved most every minute of it. Good luck to you.

What exactly do you do?
My job is to evaluate manufacturing problems and support the manufacturing departments when they aren't able to properly analyze their problems.

One example of this is in our paint department. Because Honda is always striving to produce the highest quality product, we need to make sure that all of our vehicles have no paint defects when they are delivered to our customers. The way that we do this is to inspect every unit that passes through our paint shop and repair the units that have fiber in the finish. The units that require some re-work are sent through our repair area while the rest of the good bodies are sent to the good body storage. The good body storage area acts as a window of time for the unit requiring re-work to re-link into its original location insuring the bodies are in sequence. There are many variables that play into how large a good body storage area should be, so, because of the complexity of the system, I was asked to study and determine the appropriate number.

Describe a typical day.
My typical work day has a nice balance of engineering work done behind a computer, where I will study a particular problem, with frequent trips to the manufacturing floor to go to the actual spot to determine the actual problem.

The majority of the information that is required to adequately address a problem isn't readily available. Because this is usually the case, we need to setup methodologies for how to collect the data. This sometimes involves creating project teams in specific areas so we are able to draw on the expertise in that area or physically collecting the data every day. Even if there is a system in place to collect the data we always need to validate the information before we are able to use it in our study.

What's the coolest part of your job?
The best part of my engineering career is the ability to use my technical abilities creatively. Going through high school and college prepares you technically and gives you the skill sets and tools required to troubleshoot and solve problem, but after that it is our responsibility to know what technique to use and when to apply them. Learning what approach to take and what theory to use will make the difference between fixing a problem and coming up with a robust solution to alleviate a problem.

How do people react when they learn what you do?
The most common question when I tell people that I am an engineer is "Where is your train?" Sorry for the bad joke.

The majority of the time I tell people that I work at Honda using computer-based simulation packages to test equipment designs before we purchase them, and people ask me where I learned to do that. I learned the fundamentals of statistics and probability and some general concepts of discrete event simulation at college. I didn't learn how to apply the concepts that I was learning until an internship I had with Honda while I was still at college. The real world application of my studies reinforced my decision to become and Industrial Systems Manufacturing Engineer.

How did you become an Industrial Systems Manufacturing Engineer?
In high school I decided that I would like to give engineering a try. I didn't have any particular engineering discipline in mind but I wanted to take a closer look at all of them before I decided. When I enrolled in college the first quarter I was considered Engineering Undecided. To me that wasn't a big deal because the first year and a half college students in engineering, indeterminate of the specific discipline, take the same course work. After I took a Fundamentals in Engineering Course, which went through all of the engineering backgrounds I decided that Industrial and Systems Engineering was the best fit for me because it provided the business aspect as well as the engineering background.

What disappoints you about your job?
Because my current group acts as a support function, we generally provide recommendations to the department, and we don't have any responsibilities in actually installing or implementing our countermeasures. This happens for two reasons. Because we aren't involved directly with production in the areas we do projects for, we need buy in and ownership of the countermeasures by the departments we are helping.

The second reason is by the time we are completing one project we are already starting up another project, which means that we generally don't have time for the implementation, testing and debugging.

How has your job changed over time?
I have changed my role slightly since I first started. I am now not only taking on projects myself but mentoring and training others in my group and departments of how to approach a project and what steps in a project help facilitate a successful countermeasure. This is a nice change of pace because it allows me to break up the project work with developing fellow associates capabilities in a variety of backgrounds.

How will your job be different ten years from now?
Ten years from now automotive companies will be challenged with trying to be profitable through a much greater model mix. Currently we are constantly challenging our groups to make our manufacturing characteristics as lean as possible.

In the future we will have to be able to develop many different models on a common assembly line. This will give us new concerns in trying to maintain and increase our process efficiencies so we can continue to be profitable as a company. These challenges will force us to become more creative in our ideas and our ability to manufacture our cars and trucks. I, as well as everyone at Honda, will have to be adaptive and responsive to what our customers want so that we will be able to exceed their expectations.

What are some of the most important skills and abilities needed for this job?
The most important skill needed for this job is a systematic problem solving approach. Having the correct problem solving approach, that is repeatable, will allow you to break down even the most complex problem with limited knowledge of the equipment or process up front.

A willingness to learn new things and be open to suggestions from fellow associates will only help the solution to a problem be accepted. Communication is also one of the most valuable skills to have. Even the best idea in the world will not be accepted if you don't have the ability to convey the importance and urgency of the solution.

The only other thing that you will need, after you graduate college of course, would be the motivation to succeed. Motivation to succeed and do well is entirely based on your own personal drive. This is a character trait that will raise you above the rest of the group when schedules are tight and deadlines are rapidly approaching.

What advice do you have for people who want to enter this field?
My advice to all of you in your career decisions is to gain as much exposure as you can in the field you are interested in. Just like you wouldn't want to buy something you have never seen before, you also don't want to select an occupation based off of what you have read about in a book. Experiencing the job through a job shadow day or through talking with people that are currently doing the job is invaluable.

Based on what I did & observing other engineers in 2 industries, a typical day includes following up on current assignments & addressing new challenges. You will be asked to stop what you are doing at any time & investigate issues as they arise. You will sometimes use tools that you learned in school, but most of the time you will have to conduct your own research & improvise. Your best tool will always be to learn fast & know how to tap the knowledge that someone already has.