We lose the latter incentive with IPFS, and so Filecoin is replaced as the new incentive to give up storage space for the P2P network.
You can still put your content up on IPFS for free, it's just that only your IPFS node will be hosting the content, and thereby won't be truly decentralized. You're the only "seeder", so to speak.
Is hosting content the way that it is mined? Or is mining it something else?
Once implemented, you should be able to buy Filecoin from market exchanges. To earn it, Filecoin will use two "proofs-of-storage". One is "proof-of-replication" wherein your IPFS node proves to be replicating data, and "proof-of-spacetime" wherein your IPFS node proves to have stored said data for a certain amount of time.
You can read more about from their whitepaper: https://filecoin.io/filecoin.pdf