Manually changing the player role's active 'from' and 'to' dates
If you edit a person and then click on the link 'Change Organisation Roles' you will see the teams the player is on.
See the following example:
Paul Smith - Team A
If you edit that person's role you can set a closed date for them of when they closed on that team and will no longer be an active player.
Paul Smith - Team A - from (open) to (today)
Then you create another role from them on their new team.
Paul - Team B
Add an 'active from date' of today and leave the end date open i.e. blank
Using the Player Transfer tool
In the main menu go to:
People > Transfer > Transfer Players
This tool automatically applies the active 'from' and 'to' dates to player roles. Sometimes it will be easier to do it manually first so you understand how it works.
Reasons why a player might appear on a team
Players will show on the team page on the league website if they are active on a team for any part of that season.
They will show on match pages on the league website if they are active on the team for that match or have stats entered.
They will also show on the stat leaders page when they have stats entered for a team irrespective of whether they are still active on the team now.