Basically @m1xolyd1an answered it, I extend it a bit. So you would have a funding transaction, which send some satoshis into the multisig transaction. Usually to a "type 3" address, which is the hash of the redeemscript, converted into a bitcoin address.
Then you want to spend this transaction, and the conditions are outlined in this redeem script. You provided the script already, the part of the redeemscript would look for a 2-of-3 like this:
You would then create a first tx ("createrawtransaction") to sign it ("signrawtransaction"), and then take the resulting hash to sign with the other private key which increases the length of the tx. And then you'd send it to the network. You can redo this fairly easy example on testnet or on your regtest env, Gavin provided a very good step-by-step example long ago.
Who puts second signature into the script?
This can be yourself, when you use a cold storage concept, this can be a second person, to which you give the hash to get it signed.
Oh, as this is very basic of bitcoin, I recommend also to have a look at Andreas' book "Mastering Bitcoin", in chapter 7 on multisig. The book is online readable.