One of the most common types of offerings and probably one of the most ancient is the concept of the shared meal between the household and the other world, which may be defined as the gods or the ancestors or local nature spirits. The idea here is simply to make a big family meal and leave out one extra plate with a small serving of every dish found at the table. The extra plate may be left on the table, or placed on an altar with a group prayer.
The circumstances in which you would normally leave an offering are three. You would leave an offering on a holy day, or if you want to ask the gods or the spirits for help with something, or if you want to thank them for some blessing you have recently received. For instance, if you get a bonus at work it's appropriate to leave an offering to thank the gods. The sacrificial offering is a key part of making your pagan practice genuinely religious.