First challenge is that there is no average day for my job. There is no average month or average year. That's part of what I like about it - I've moved around in the company a LOT. Technically I'm doing a time warp for this entry anyway, I'm a manager, I spend a much higher percentage of my time in meetings and I do not do any design work, but I thought it'd be more helpful to pretend I'm still a 3-5 year experience engineer, for this entry.
Here are some things I've done.
The "day" depends on program phase. If we're making a huge big new airplane we'll spend weeks at a time doing design, weeks doing testing, weeks writing reports. Once it's being cranked out on a production line we have all these random little improvements we're doing so in one day you'll do a little of everything and juggle as best you can... every hour something different. I've spent more time in "every hour is different" mode than "every month is different" mode, that's for sure. Here are the tasks:
Design: Using computer programs that I'd never heard of before I came to work here, I lay out system wiring diagrams for airplanes. We identify a component we need, then read installation manuals and sensor specs. If one box says it needs to know airspeed on a data bus, we find the other box that puts OUT airspeed on the data bus, and produce a diagram that shows them wired together, with all the disconnects needed to make airplane building easier... for example you would not want to run a wire all the way from the wingtip light straight back to the tail. We build the wing, run all the wires to one connector, so when they mate the wing to the fuselage there's just one plug to plug in. My drawing shows that.
Sitting with headphones on, drawing the diagrams, getting everything to make sense and be pretty and readable, I spent several years where that was a good chunk of my job.
Of course, that's systems integration... a lot of electrical engineers do component level, lay out PC board stuff, don't ask how I went into systems, I think it was an accident. That's the story with a good 80% of my career circumstances, it all just happened.
Testing: You know how the system works. Write a test for it. Get with the "official" people and run the test in front of them and get all the paperwork done that says you ran it for that fancy report you're writing. Sometimes you're in a lab, sometimes you're on an airplane. It's never happened at my desk. Actually I will say there's so much involved in getting the paperwork in order for an official test, that when you're testing you're testing, that is your day, no matter what phase of a program you're on.
Certification: We write reports. We have a list of federal regulations, we copy every one, we write down why we're good on it. For instance, here's a rule that says you have to make warning lights red. Our job is to prove we met it... was there a test, or can you just see from the engineering drawing, or both? On new experimental programs I spent weeks at a time when I spent 70% or so of my day working on these reports. I know you're thinking that this must be a special activity for engineers who work on airplanes, but it's also for engineers who make big structures and meet construction requirements, engineers who make medical devices and have to prove they're healthy, in fact I don't personally know any engineers who don't have to prove themselves to the government in some way or another, or at least to some industry group like UL. We type, draw pictures, dig for information, state cases, review each other's reports for checking.
Troubleshooting: The technicians plugged everything in just like you said and the fuel level doesn't show anything, what's wrong! You're getting a call, go down to the line. There are whole days you spend on the airplane.
Meetings: As a new engineer I had meetings 2-3 times a week. Now it's 3-5 times a day... but ugh, whatever, lots of meetings. Get everybody's opinions on your design, talk about the status of things, learn what's next for the group, hear what everybody has learned, there are meetings.
Phone calls and emails: The more you do the more you're the one who understands it the more calls you get. From the sales people, the marketing department, the program managers, everybody. I have no quiet days. If I ever have a quiet day I know better than to brag about it because it will bring on the curse of tomorrow being "LET'S ALL CALL SPACEFEM" day. The random questions come every day, from everywhere. I will sometimes go a day without getting a call to troubleshoot an airplane. I will NEVER have a day where I'm not digging up some answer.
Process improvements: My big company means there lots of options for streamlining things, introducing new software, writing down best practices, holding training classes. I spent a whole year where I left my avionics engineering department to work as an IT liason for engineering.
Organizing nacho day: sometimes we need a spreadsheet for a potluck, just sayin'. Or we have to decide where to go out for lunch of Friday. Office stuff. We have departments of 5-15 people and we get very close and like each other and try to have fun.
So that's it. It would be very normal for an engineer to spend 4-6 hours drawing diagrams and writing reports, 1-2 hours in meetings, 2-3 hours troubleshooting, researching, and seeing how things are going on the airplane. That would be a typical day.
Final interesting note: I didn't learn how to do any of this in college, so if this isn't what you're taking in classes, fear not. There'd be no reason to learn how we write certification reports... just learn to write. No reason to learn to test every specific kind of potentiometer setup in existence, just learn how to run a voltmeter. My dad used to say that a college degree proves you are educatable. True. It also shows you can commit to something - you won't leave a job in six months if you spent four years getting the degree for it, so you're someone we're okay training for all the big crazy stuff going on with our industry. Don't sweat it. Good engineers don't know everything. We're just gritty, scrappy, ready to learn, unlikely to break down if something goes a little weird, interested in blinky lights, and for best results... not assholes. There, you have my recipe for success at this. Go study.