How to get the most value from a career fair?

Go in and follow your curiosity. When treated as a min/max optimization, things usually fall apart (speaking from experience from my early career).

Don't try to force things and 'sell yourself'. The companies there are trying to promote awareness and let other know what they do (and why they are a desirable employer). Go with the flow and seek out information.

I find that when I go in with an open mind trying to learn about what they do, the conversation will naturally flow. After awhile, it's natural for them to reciprocate and ask about you. This is when you can give them a quick preview into your past experiences and skills.

Towards the end, offer to connect and thank them for their time.

Here are some basics:

1. Go in early - Some companies are first-come, first-serve.
2. Do research on companies - Show that you care with some homework. This alone puts you above 50% of other students.
3. Make sure your resume is clean (and bring a stack) - This is obvious.
4. Don't sleep on startups - Back in my day, the lines for big companies were so huge. You had to wait in line for 20-30 minutes just for 1 companies. Meanwhile, booths for companies like WhatsApp and Venmo (this is before they exploded) were almost empty. Getting a job is a numbers game - Go to as many booths as possible and make calculated decisions about the time investment behind big companies.

Companies will often send engineers for career fairs as well. Those are always fun!

I cover this more in my blog post here: How To Find A Job As A Computer Science Student

I was going to ask what is the best way to approach recruiters from each company and what type of questions would you ask?

Just walk to them and start a friendly conversation as you normally would. Be interested in them. If you have done #2 from the above list, you can even lead with something about their company and ask what they think of it (e.g. "So your company just announced its AI integration for XYZ, what do you think is the future of that product?").

I recommend going through the deep listening part of my Effective Communication series as well: Effective Communication Guide [Part 3.2] - Deep Listening