There are two ways to do it in a standard transaction format that will be relayed by full nodes. However, if you are a miner you will have more leeway into the scripts that you can use to lock your transaction. However, doing this is strictly discouraged as it adds to the UTXO and blockchain bloat in the first case and blockchain bloat in the second case. This answer is meant just for educational purposes.

Trick 1: create a bare multi-sig output (not P2SH) and sending some non-dust value to that base multi-sig address. You would use the bare multi-sig format for encoding like M <pub_key_1> <pub_key_2> ... <pub_key_N> N but here the pubkeys between OP_M and OP_N will be your data that you want to encode padded to the public key length. However, you can lock only up to 3 keys in bare multi-sid which will be 65*3 = 195 bytes. Again I mention that this method is discouraged as it adds to the UTXO bloat.

Trick 2: A better and cleaner way to do it will be to lock some BTC in a hash of the data you want to store encoded in a P2SH address. Then spend these bitcoins where the unlocking script will be the data that you want to store on the blockchain. In this case you can lock a much bigger data but care has to be taken not to exceed 400,000 WU for the overall transaction for spending as it would make the transaction non-standard.