If I'm Connected To Wi-Fi On My iPhone 6 Will It Use Data?

I believe I misunderstood what the guy was telling me about my plan. I thought he was saying he only has 3GB on his iphone for internet data usage bc usually where he is at there's Wi-Fi… Meaning he uses his computer instead of his phone for the internet most of the time.

But… Did he mean that as long as you are connected to Wi-Fi you can be on the internet as much as you want without it going towards your data usage?

He said something about the reason why Verizon doesn't offer unlimited internet anymore is it made it run slower for everyone… Or something, lol. I was so lost…

No. Typically it will not use up your company's data limit if you're connected to random Wi-Fi at some place like Starbucks or McDonalds or through someone else's computer or phone. You will be using up their data from their service provider. You use up your data if you connect directly from your phone or computer through your service provider.
Companies like Verizon will limit the amount of data you can use per month for high speed internet. If you use more than that they will reduce the connection speed or make you pay for more data.

If you are connected with a Wi-Fi then it will use Wi-Fi as the first source and if the Wi-Fi is not working then it will use data consumption.

If you are using Wi-Fi, then you aren't using data.

Look at the top and it tells you how you are connected, or if really concerned you can turn cellular off and Wi-Fi on, then you know for sure you aren't using data plan.