there are a few components to it: you need to know the type of script you used to create the address, you need to know the keys and policies involved in the script, and you need to use a wallet that can build the script and sign transactions for it.

take a 2-of-3 p2sh multisig for example. if you created this script with electrum, you went through a process to set up the multisig. electrum has a gui that walks you through the process, it asks you what the signing policy is and what the xpubs of the signers are, and from that it can create the wallet, derive all of the addresses, and build txs to sign. so in the case of this multisig wallet you need to know that it's 2-of-3, p2sh, and the specific 3 xpubs used. with this information you should be able to recreate the wallet in any application that supports creating p2sh multisig wallets.

for more advanced scripts, you might need to know/backup more information related to the spending conditions. and if you lose that information, then you lose access to your funds.