To invest in XCP and Counterparty, switch Bitcoind/Bitcoin-Qt and counterpartyd over to mainnet simultaneously. Use the command-line switch -testnet=0 with Bitcoind or remove any 'testnet=1' from the Bitcoind configuration file temporarily; then do the same for counterpartyd by both not using the --testnet flag and (again, temporarily) removing 'testnet=1' from counterpartd.conf.

Make sure that Bitcoind and the counterparty server are running, and then run ./counterparty --rpc-password=PASSWORD burn --from=ADDRESS --quantity=QUANTITY, where 'PASSWORD' is the password used to access Bitcoind's RPC interface, 'ADDRESS' is an address in your Bitcoind wallet with sufficient bitcoins, and 'QUANTITY' is the quantity of BTC that you would like to burn.

No more than 1 BTC may ever be burned by any address, and the number of XCP received per BTC is between 1000 and 1500, with more XCP being rewarded the earlier in the burn period the burn takes place. The burn period is 5000 blocks, starting today, and the reward bonus decreases linearly with block index.

To see how many BTC you have burned, and how many XCP you have earned, run ./counterparty --rpc-password=PASSWORD address ADDRESS.

Of course, you can burn Test BTC on testnet to have XCP to play with there.

To get a rough idea of how many BTC have been burned so far, see https://blockchain.info/address/1CounterpartyXXXXXXXXXXXXXXXUWLpVr. Note that this page may show some false positives. You cannot just send bitcoins to that address with any client and expect to have them be properly burned. For more instructions on how to burn, e.g. with a Blockchain.info wallet, see Read The Docs.