One option is to hijack a prefix by announcing a more specific one. This should then route traffic to the more specific prefix to your AS. You can then analyse and forward the traffic, attempt to impersonate a server within this range or simply drop the incoming packets.

As the author described, this case might be a bit more tricky, as BGP prefers shorter routes to longer ones. However, it seems that some longer-than-necessary routes were in use.

I kind of understand what's the use of BGP, but the article was lacking too many details even for me. cloudflare has a better article, their conclusion is that this was probably an accident and not an attack, because the leaked routes were so low priority that it couldn't cayse traffic to be rerouted.
they didn't say but I think perhaps what it could have done is overload the venezuelan state ISP with traffic they shouldn't handle, but I don't know for sure

https://blog.cloudflare.com/bgp-route-leak-venezuela/

Made perfect sense to me. Messing with how edge routers would talk to upstream pipes would indicate some attack.