What's the difference between 'Ser' and 'Estar'?

This is common confusion for many Spanish students. Both verbs mean 'to be' in English, but have different uses in Spanish! Here's a very general go-to rule to help you remember which verb to use when: 'Ser' is used to describe permanent states and 'Estar' is used to describe temporary states (both temporary and Estar have a 't' in them - that helps me remember the pair quickly). This quick rule can be seen as rather vague though, so a good way to remember their uses in more detail is through acronyms.
For 'Ser', the acronym DOCTOR is commonly used. This stands for Descriptions, Occupations, Characteristics, Time, Origin and Relationships. Taking the example of characteristics, to say 'I am a happy person', you would say 'Soy feliz'.
For 'Estar', the acronym PLACE is commonly used. This stands for Position, Location, Action, Condition and Emotion. Taking the example of emotion, to say 'I am feeling happy', you would say 'Estoy feliz'.
Note the difference between this and 'Soy feliz' as written earlier. Using 'Ser' implies that I am always happy, or that happiness is a permanent characteristic of myself. In contrast, using 'Estar' implies that I am temporarily happy, or that I am just happy at this moment.
An important exception to note is that while 'Estar' is used for locations, it is not used for events. So while you might say 'el estadio está en Londres' (the stadium is in London), you would say 'el partido es en Londres' (the match is in London), since the match is an event.