How is punishment for a red card decided?

If a Player is sent off, it is a matter of fact the Player will be suspended 7 days after the date of the game, as set out by The FA in the Discipline Handbook.

The length of ban depends on the type of misconduct: 

Serious Foul Play

3 match suspension

5 penalty points

Violent Conduct

3 match suspension

6 penalty points

Spitting at an opponent

6 match suspension

7 penalty points

Denies an obvious goal scoring opportunity by an offence punishable by a free kick or penalty kick

1 match

3 penalty points

Denying an obvious goal scoring opportunity by deliberately handling the ball

1 match

3 penalty points

Use of offensive, or insulting or abusive language

2 matches

4 penalty points

Receiving a second caution in a match

1 match suspension

3 penalty points

You can read more about misconduct charges in the Discipline Handbook.