Layer 3 switches basically have the ability to route packets using the same criteria that a router uses, but in hardware so its an awful lot faster than a standard router.
Most people buy a router to connect to a low speed WAN circuit like a 2Mbit Serial link or anything under 10Mbit... Any of the high end routers such as Cisco 7609s GSRs etc, are basically switches labeled as routers as everything is done in hardware.
In the case of your 3750s you can actually configure the interface with an IP address exactly the same was as you can with a router, its basically a router with gigabit ports and loads of them, the principle is the same just many times faster hence why they're used in the core, just treat them like routers.
Normally the access layer of the network <2950s or whatever make> will be layer 2 only and will have Vlans and access ports, with a trunk port connection to the upstream distribution switches, these normally have Vlan interfaces which is a software interface configured with an IP address which will be the default gateway for people on that Vlan at the access layer, the distribution switches will then normally connect to a core layer which runs strict layer 3 routing between the rest of the core and other distribution switches, there are loads of examples of this in on the Cisco site, its a pretty well known base design for most largeish lans,