When an IP or a block of IPs are assigned to you, do the network admins just add them to a router?

Let's say there is a router to the internet and a router separates your network from others within a data center.

When the data center provided gives you IP addresses, do they just take a [set] of IPs they own and enter a route in their router to your router?

Solution 1:

IP Addresses are issued from a central authority, the Internet Assigned Numbers Authority. This organization handles centralized numbering for many internet resources, including registering port numbers for services and also keeping track of internet-related numbers such as ISN/ITADs for Telephony routing over IP (Current List of registered ITADs.) Various organizations across the globe, called Regional Internet Registries (RIR's) make requests of the IANA to receive IP address space that they can then allocate to ISP's and end-users.

When you or your ISP make a request for IP address space from an RIR, the RIR officially allocates the IP address space to you or your ISP, at which point the registered organization would send a BGP advertisement for that registered IP space to their ASN. Once this has been completed, the internet has now been notified (after a brief period where BGP synchronizes) that those IP addresses are transiting to a particular location.

At this point, the IP traffic is traversing to the router where the BGP advertisements are occuring. From this point, if the operator is an ISP, they would then route you whatever IP space you requested through your existing links. If you are the operator, rather than the ISP, it would be your choice how that IP space was routed after it hit your edge router running BGP.

Solution 2:

The general answer to your question is "yes", assuming they're assigning IP addresses to you that they are already routing on their own network. Typically, they add the route only on the router that faces you, directing the IP block they just assigned you either to the interface that connects to you or to the IP address assigned to your side of your link to them. Their interior routing protocol takes care of the rest, propagating that route throughout their own network as far as needed until the covering, aggregate route takes over.