Go to the homepage of the app (tap the Assets tab) and swipe up
Tap on the token you want to send (e.g. ETH)
Select the contact or enter a new address
Choose the amount
Tap Network fee to change the transaction speed or the token you pay the fee in.
New destinations: When sending an asset from Argent to a new destination, please check the destination accepts transactions from Ethereum smart contract wallets. Some wallets/exchanges do not. If Etherscan shows a transaction succeeded but you can't see them, please refer to this post.
Tokens: Check the destination address supports the assets you want to send. Not all exchanges accept DeFi investment tokens, for example.