PHP multiple checkboxes

I'm slowly back into coding ...

I'm getting race data from a database, and based on a field, I check or don't check a checkbox

For example

[ ] Race 1
[x] Race 2
[ ] Race 3

Each race can be on/off. So, I could change it to:

[x] Race 1
[x] Race 2
[x] Race 3

I'm having trouble to construct my form and send the data to change my database to reflect the choices.

Hope the explanation is clear !