They connect to the internet like everyone else does, except they don't have to pay an ISP to do so, as they are the highest level of ISP.
How the internet works is like this, there is a bunch of datacenters that have servers. Each datacenter that wants to communicate with each other, utilizes a point to point connection, meaning they have physical cables running between the datacenters. ISP's have their own small datacenters albeit to handle their network where they provide Internet access, that connect to these largers ones.
So the ISP, pays for the use of the higher ups, network to other datacenters or lines they don't own. So, Tier 1's are not necessarily ISP's per say although you can view them like one, they are the ones that own the cable or fiber optic lines that go between geographic locations, as oppose to owning the cables or fiber optic lines in a specific town although they can as well.
Each ISP has its own Point to Point connection to the closest datacenter they provide internet access to, the Datacenters in the region have point to point connections between each other as well sometimes having Point to Point connections to datacenters outside their region but usually the datacenters in the region connect to a very large datacenter closest to them, and then those large datacenters connect to each other, although it doesn't strictly have to be that way, just for the sake of explaining thats how it works. So, the Tier 1 provider, or the datacenter, connects to the internet like everyone else does, with the execption they go through fewer connection points to do so and they don't require a modem to do so either.