Some or all of what I say here may have been said before. I've been dabbling in crypto since the early 2010s. I have also done exactly what this thread is about and now have N. I cannot speak to processes outside of the US.
The easiest way by far is signing up for one of the exchanges and then buying crypto from that exchange. One that is used is Kraken. You can purchase monero directly on kraken. They will want lots of personal info. There's no way around this if you want the easy way. You will have to give your SS at minimum and they will verify your identity. This is not the way to go if you're trying to be completely anonymous, and I have no suggestion on that as idgaf who knows I trade crypto.
Next, kraken will assign you a wallet. Wallets have 2 parts, both very long strings of letters and numbers. The first part is the private key. This is the key that says that you're the owner. Think of it as the code to a safe inside your house. The second part is a public key. Think of the public key as your home address. The address shows how people can get to you but just because they can get to your house doesn't mean they can get into your safe. Same concept.
The concepts I state here are just ways of explaining how crypto works. They can't really find out your actual house address. Just wanted to state that in case someone thinks I'm being literal.
When transferring money, you get the public key from the person you're sending the money to. It's like youre going to deliver the money yourself to their address. Kraken let's you send monero directly from your account to their account. Again, this does leave a paper trail to you because you're sending it from kraken*.
TL;DR
So, to sum, sign up for kraken. Once you're completely verified yourself, buy monero. Whoever you're buying N from, they will give you a public key. You send monero to that key via Kraken. The other side should verify they got the funds, then send your product.
If you solely use Kraken, you will never see your private key as Kraken takes care of all that for you. Using online exchanges takes out a huge amount of work when dealing with crypto. But again, just to stress, there are drawbacks.
I will not disclose any details of my transaction except to say this is how I did it.
* - there are ways of doing this by more anonymous means, but this requires you to download a "wallet" to your computer. It's complicated. Exchanges take care of all this for you.
If you want to be fully and totally anonymous, you need to create at least 1 wallet outside of kraken and transfer your monero to that address before sending it out to the person you're buying N from. This is why I say it's much more complicated. I would compare this way to money laundering. Again not literally, but you're creating a "shell" address that you use to pass through all of your funds before sending them to someone else. I can detail this, but I am stressing that it's not easy. It's complicated and a bit more technical.