In the open market you either get transit (you buy bandwidth from a carrier) or peer (you exchange traffic with a provider) with other networks.
There are also IXs, where you can peer with a lot of different networks in one place (DE-CIX is the biggest for example, located in Frankfurt).
Transit is billed 95th percentile, that means if you want to commit to 1 GbE on a 10 GbE uplink you pay the 1 GbE outright and can burst to the 10 GbE the uplink provides you. If you are over 1 GbE at the end of the month (95th) you will be billed the remaining mbps with a per mbps pricing.
Now, to answer your question, it basically works like that:
You are present in NYC and you want to reach a customer on the west coast that uses Comcast. You would buy transit in your NYC facility from Comcast to get a direct path/way to them. They will take care of everything else. You don't have to lease/rent/buy the dark fibre (cables) from the east to the west coast, the provider (in this case comcast) is doing that already. If you don't buy transit from comcast, but instead form some cheap carrier (say cogent) they will do the same BUT not guarantee a specific bandwidth to comcast, you only would get 10 GbE to cogent, but you don't know if you can push the 10 GbE to comcast.
Transit providers also vary vastly on price. DTAG (Telekom) for example is ridiculously expensive (5x the prices of regular transit providers).
Let's say you want an decent pipe (transit) with 1 GbE commit on 10 GbE, you would pay something like $500-$600 for the 1 GbE commit and after that around $0,50 per every additional mbps. Additionally you need a router, preferably two (redundancy). Fiber cables, transceivers, etc. All those things are very expensive.
What you also notice is that you can't get transit with a TB billing, but most providers offer you per GB/TB billing. They need to commit to a certain amount and hope they calculated well in regards to their commitments and usage etc etc. Anyways, $80-120 per TB, the cloud providers are charging, is a bad joke.