When your free trial on any of the plans expires you will see a green bar at the bottom of the screen asking you to purchase.  If you click on the purchase button you will be prompted to select a plan, and then for credit card details - if you have any confusion around the options, please read this article explaining the various pricing plans.

I want to purchase but I don't see the notification anymore

If you have cleared the green purchase notification at the bottom of the screen, in order to purchase you will need to do one of the following:

Open the settings screen and click on the team name that you want to upgrade:

Click the upgrade or change button:

If you don't see an Upgrade or Change button it means that you are not an Admin of the team and you will need to ask the person who invited you to the board to upgrade the account or to add you to the Admin group so that you are able to upgrade.

Choose whether you want to be billed annually or monthly, check the Terms of Service, select a plan by clicking the appropriate "Buy for..." button and capture your credit card details.