When using the hudson git plugin with https, how to I specify a password?
You can't. It is bug in git plugin, but there is fork that fixes it, see:
http://issues.hudson-ci.org/browse/HUDSON-3807
The status as of this writing is that you can.
There are at least two ways of doing it:
netrc approach is by default a plain text file. If needed, it can be encrypted as explained in this answer, or just be readable for that one user through permissions.