Once you approve a token, you will not have to to approve that token again on the Uniswap web app. Each token from a specific wallet you wish to trade requires a one-time approval.
When swapping tokens on Uniswap Protocol, you will see the following message:
Once you select the Allow icon you can proceed to swap your tokens.
When you approve a token, it is considered a transaction so you will have to pay a network fee.