The easy answer?
Only when you need to.
The longer answer ?
Speed Ups, and their close cousins, the Production Items, allow you to do a lot in a little time. You use them when you need to do this.
When building your first city, during your 7 days of protection, most of your development holdups will consist of either not enough resources for the next project, or having to wait for the first project to finish. This is one of the two best times to use the speed ups.
Build your resources in your first session, then apply the Production Items to max out resource production
Do NOT use your Speed Ups early to plunge through those first 1 minute builds. Wait until you are doing Level 4 upgrades to apply Beginner's Guidelines.
If you are developing on schedule, you can probably get full use out of all your starting Speed Ups on Day 7.
The other use for Speed Ups is when recovering after an attack, or in some cases preparing for an attack. If you see an attack coming, and you know that you'd be able to crush it if only your Archers would finish training in time, then by all means use that Napoleon's Diary to hurry things along.