There are 4 types of Speed Ups. One is to speed up the building you are constructing, one is to speed up the Technology you are researching, one is to speed up the time of Travel for your merchants, and the last is to speed up the Troops you are building.
There are 9 types of Guidelines that you can purchase/win/find. You can find them here: Guidelines.
Speed Up for Buildings can be done for free for any build time less that 5 minutes. NOTE: Sometimes it looks like you are building under 5 minutes but the system will not allow you to do it for free. The reason for this is because either you have researched the Technology of Construction or your Hero's Politics.