To move bitcoin from the exchange to your own custody.
You need a wallet.
There are 2 kinds of wallet, hot or cold.
Hot just means that you have the wallet on your computer, or phone.
Cold means your wallet is on a dedicated usb, which is not connected to the internet.
Most people have both hot and cold, the hot wallet will generally have a very small amount of coin for everyday use, whilst major funds are kept in the cold wallet.
The reason for people having both is the fact that if your computer is hacked, or stolen your bitcoin is at risk.
HOT WALLLET
There are many brands of hot wallets I use Electrum available from electrum.org, they are free and you do not need any coin to download wallet.
COLD WALLET
Again many different brands, most popular are Trezor and Ledger. These cost around £80
Do not be tempted to buy on ebay etc, as they can be tampered with, only buy from official company.
SETUP
Whatever, hot or cold the setup is the same and simple.
Follow the instructions at each step, and remember they are not joking when they ask you to write down the seed phrase they will provide you with.
At the end of setup they will ask you to choose a password.
So you now have a password and seed phrase (a seed phrase is 12 words provided by the wallet)
to get your head round this just think the following>
The password relates to the actual device your wallet is on(computer, phone, Trezor, etc), and the seed phrase is not needed whilst you are using the original device.
The SEED PHRASE though is the be all and end all.
If you lose access to the original device, you can regain access by just installing another wallet and entering the seed phrase.