ASAP.

some committees give you the check to send to the school, and some may want to send it to the school directly.

also, important look at scholarship deadlines, that will also tell you.

Each scholarship will have its own deadline, but ideally - do it as soon as you can. You don't want to get lost in the last-minute applications of others. This may require you to "guesstimate" portions, but you can make that clear when you submit the paperwork (and indicate you'll send follow-up copies of transcriptions, once grades come in, etc.)

Getting paperwork in early also gives you some back-up time in case you have mislaid some part of the application, or they require any clarification.

I know in my line of work - the first few applications that come in get a better review than the flurry of late applications; and I assume that holds true for scholarship applications.

You should start applying as soon as possible (like now) so you will be one step ahead of everyone else. It never hurts to apply early, but you might miss out if you apply too late.

And here are some good grant and scholarship sites:

Good luck!